@article {Abh,
    AUTHOR = {Abhyankar, S.},
     TITLE = {Local uniformization on algebraic surfaces over ground fields
              of characteristic {$p\ne 0$}},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {63},
      YEAR = {1956},
     PAGES = {491--526},
      ISSN = {0003-486X},
   MRCLASS = {14.0X},
  MRNUMBER = {0078017 (17,1134d)},
MRREVIEWER = {P. Samuel},
}

@preamble{
   "\def\cprime{$'$} "
}
@book {Ar,
    AUTHOR = {Arnol{\cprime}d, V. I. and Guse{\u\i}n-Zade, S. M. and
              Varchenko, A. N.},
     TITLE = {Singularities of differentiable maps. {V}ol. {I}},
    SERIES = {Monographs in Mathematics},
    VOLUME = {82},
      NOTE = {The classification of critical points, caustics and wave
              fronts,
              Translated from the Russian by I. Porteous and M. Reynolds},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1985},
     PAGES = {xi+382},
      ISBN = {0-8176-3187-9},
   MRCLASS = {58C27},
  MRNUMBER = {777682 (86f:58018)},
}

@article {Artin,
    AUTHOR = {Artin, M.},
     TITLE = {Some numerical criteria for contractability of curves on
              algebraic surfaces},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {84},
      YEAR = {1962},
     PAGES = {485--496},
      ISSN = {0002-9327},
   MRCLASS = {14.18 (14.20)},
  MRNUMBER = {0146182 (26 \#3704)},
MRREVIEWER = {M. Rosenlicht},
}
	
@incollection {BaPo,
    AUTHOR = {Batyrev, V. V. and Popov, O. N.},
     TITLE = {The {C}ox ring of a del {P}ezzo surface},
 BOOKTITLE = {Arithmetic of higher-dimensional algebraic varieties (Palo
              Alto, CA, 2002)},
    SERIES = {Progr. Math.},
    VOLUME = {226},
     PAGES = {85--103},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {2004},
   MRCLASS = {14J26},
  MRNUMBER = {2029863 (2005h:14091)},
MRREVIEWER = {Hideo Kojima},
}



	
@book {Beauville,
    AUTHOR = {Beauville, A.},
     TITLE = {Complex algebraic surfaces},
    SERIES = {London Mathematical Society Student Texts},
    VOLUME = {34},
   EDITION = {Second},
      NOTE = {Translated from the 1978 French original by R. Barlow, with
              assistance from N. I. Shepherd-Barron and M. Reid},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1996},
     PAGES = {x+132},
      ISBN = {0-521-49510-5; 0-521-49842-2},
   MRCLASS = {14Jxx (14-02)},
  MRNUMBER = {1406314 (97e:14045)},
}

@misc {BCHM,
    AUTHOR = {C. Birkar and P. Cascini and C. D. Hacon and J. M\textsuperscript{c}Kernan},
     TITLE = {Existence of minimal models for varieties of log general type },
      YEAR = {2006},
      NOTE = {arXiv:math/0610203},
}

@incollection {Bri,
    AUTHOR = {Brieskorn, E.},
     TITLE = {Singular elements of semi-simple algebraic groups},
 BOOKTITLE = {Actes du Congr\`es International des Math\'ematiciens (Nice,
              1970), Tome 2},
     PAGES = {279--284},
 PUBLISHER = {Gauthier-Villars},
   ADDRESS = {Paris},
      YEAR = {1971},
   MRCLASS = {32C40 (14B05 20G20)},
  MRNUMBER = {0437798 (55 \#10720)},
MRREVIEWER = {Jonathan M. Wahl},
}

@article {Brow,
    AUTHOR = {Browning, T. D.},
     TITLE = {The density of rational points on a certain singular cubic
              surface},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {119},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {242--283},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {14G05 (11G35 11G50)},
  MRNUMBER = {2250046 (2007d:14046)},
MRREVIEWER = {Ulrich Derenthal},
}
		

@article {Cay,
   AUTHOR = {Cayley, A.},
    TITLE = {A Memoir on Cubic Surfaces},
   JOURNAL = {Philosophical Transactions of the Royal Society of London},
   VOLUME = {159},
   YEAR   = {1869},
   PAGES  = {231-326},
}

@article {CKM,
    AUTHOR = {Clemens, H. and Koll{\'a}r, J. and Mori, S.},
     TITLE = {Higher-dimensional complex geometry},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {166},
      YEAR = {1988},
     PAGES = {144 pp. (1989)},
      ISSN = {0303-1179},
   MRCLASS = {14J30 (32J99)},
  MRNUMBER = {1004926 (90j:14046)},
MRREVIEWER = {Peter Nielsen},
}

@article {CTS,
    AUTHOR = {Colliot-Th{\'e}l{\`e}ne, J.-L. and Sansuc, J.-J.},
     TITLE = {La descente sur les vari\'et\'es rationnelles. {II}},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {54},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {375--492},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G35 (14G25)},
  MRNUMBER = {899402 (89f:11082)},
MRREVIEWER = {Daniel Coray},
}


@inproceedings {CT86,
    AUTHOR = {Colliot-Th{\'e}l{\`e}ne, J.-L.},
     TITLE = {Arithm\'etique des vari\'et\'es rationnelles et probl\`emes
              birationnels},
 BOOKTITLE = {Proceedings of the International Congress of Mathematicians,
              Vol. 1, 2 (Berkeley, Calif., 1986)},
     PAGES = {641--653},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1987},
   MRCLASS = {11G35 (11E76 14G05 14J26)},
  MRNUMBER = {934267 (89d:11051)},
MRREVIEWER = {Andrew Bremner},
}

@article {Cox,
    AUTHOR = {Cox, D. A.},
     TITLE = {The homogeneous coordinate ring of a toric variety},
   JOURNAL = {J. Algebraic Geom.},
  FJOURNAL = {Journal of Algebraic Geometry},
    VOLUME = {4},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {17--50},
      ISSN = {1056-3911},
   MRCLASS = {14M25},
  MRNUMBER = {1299003 (95i:14046)},
MRREVIEWER = {Mina Teicher},
}



@article {dlB,
    AUTHOR = {de la Bret{\`e}che, R.},
     TITLE = {Sur le nombre de points de hauteur born\'ee d'une certaine
              surface cubique singuli\`ere},
      NOTE = {Nombre et r\'epartition de points de hauteur born\'ee (Paris,
              1996)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {251},
      YEAR = {1998},
     PAGES = {51--77},
      ISSN = {0303-1179},
   MRCLASS = {11G50 (11G35 14G25)},
  MRNUMBER = {1679839 (2000b:11074)},
MRREVIEWER = {Boris {\`E}. Kunyavski{\u\i}},
}

@article {dlBBD,
    AUTHOR = {de la Bret{\`e}che, R. and Browning, T. D. and
              Derenthal, U.},
     TITLE = {On {M}anin's conjecture for a certain singular cubic surface},
   JOURNAL = {Ann. Sci. \'Ecole Norm. Sup. (4)},
  FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
              Quatri\`eme S\'erie},
    VOLUME = {40},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {1--50},
      ISSN = {0012-9593},
     CODEN = {ASENAH},
   MRCLASS = {11D45 (11D25 11G35 14G25 14J20)},
  MRNUMBER = {2332351 (2008e:11038)},
MRREVIEWER = {D. R. Heath-Brown},
}


@article {De,
    AUTHOR = {Derenthal, U.},
     TITLE = {Universal torsors of del {P}ezzo surfaces and homogeneous
              spaces},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {213},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {849--864},
      ISSN = {0001-8708},
     CODEN = {ADMTA4},
   MRCLASS = {14J26 (14M17)},
  MRNUMBER = {2332612 (2008i:14052)},
MRREVIEWER = {Mark Gross},
}

@misc {De2,
    AUTHOR = {Derenthal, U.},
     TITLE = {On the {C}ox ring of {D}el {P}ezzo surfaces},
      YEAR = {2006},
      NOTE = {arXiv:math/0603111v1},
}


@misc {De3,
    AUTHOR = {Derenthal, U.},
     TITLE = {Singular {D}el {P}ezzo surfaces whose universal torsors are hypersurfaces},
      YEAR = {2006},
      NOTE = {arXiv:math.AG/0604194},
}

@article {DV,
author="Du Val, P.",
title="{On isolated singularities of surfaces which do not affect the conditions
    of adjunction. I.}",
language="English",
journal="Proc. Camb. Philos. Soc. ",
volume="30",
pages="453-459",
year="1934",
keywords="{algebraic geometry}",
}

@article {Dur,
    AUTHOR = {Durfee, A. H.},
     TITLE = {Fifteen characterizations of rational double points and simple
              critical points},
   JOURNAL = {Enseign. Math. (2)},
  FJOURNAL = {L'Enseignement Math\'ematique. Revue Internationale. IIe
              S\'erie},
    VOLUME = {25},
      YEAR = {1979},
    NUMBER = {1-2},
     PAGES = {131--163},
      ISSN = {0013-8584},
     CODEN = {ENMAAR},
   MRCLASS = {14B05 (32B30 32C40 57Q45 58C27)},
  MRNUMBER = {543555 (80m:14003)},
MRREVIEWER = {P. Orlik},
}
		
@article {EKW,
    AUTHOR = {Elizondo, E. J. and Kurano, K. and Watanabe,
              K.},
     TITLE = {The total coordinate ring of a normal projective variety},
   JOURNAL = {J. Algebra},
  FJOURNAL = {Journal of Algebra},
    VOLUME = {276},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {625--637},
      ISSN = {0021-8693},
     CODEN = {JALGA4},
   MRCLASS = {14C20 (13C20)},
  MRNUMBER = {2058459 (2005b:14013)},
MRREVIEWER = {Gerhard Pfister},
}



@article {Fou,
    AUTHOR = {Fouvry, {\'E}.},
     TITLE = {Sur la hauteur des points d'une certaine surface cubique
              singuli\`ere},
      NOTE = {Nombre et r\'epartition de points de hauteur born\'ee (Paris,
              1996)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {251},
      YEAR = {1998},
     PAGES = {31--49},
      ISSN = {0303-1179},
   MRCLASS = {11G50 (11G35 14G25)},
  MRNUMBER = {1679838 (2000b:11075)},
MRREVIEWER = {Boris {\`E}. Kunyavski{\u\i}},
}


@book {FH,
    AUTHOR = {Fulton, W. and Harris, J.},
     TITLE = {Representation theory},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {129},
      NOTE = {A first course,
              Readings in Mathematics},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1991},
     PAGES = {xvi+551},
      ISBN = {0-387-97527-6; 0-387-97495-4},
   MRCLASS = {20G05 (17B10 20G20 22E46)},
  MRNUMBER = {1153249 (93a:20069)},
MRREVIEWER = {James E. Humphreys},
}
	

	

@article {GHS,
    AUTHOR = {Graber, T. and Harris, J. and Starr, J.},
     TITLE = {Families of rationally connected varieties},
   JOURNAL = {J. Amer. Math. Soc.},
  FJOURNAL = {Journal of the American Mathematical Society},
    VOLUME = {16},
      YEAR = {2003},
    NUMBER = {1},
     PAGES = {57--67 (electronic)},
      ISSN = {0894-0347},
   MRCLASS = {14M20 (14D05 14D22)},
  MRNUMBER = {1937199 (2003m:14081)},
MRREVIEWER = {Alexandr V. Pukhlikov},
}

@book {Hart,
    AUTHOR = {Hartshorne, R.},
     TITLE = {Algebraic geometry},
      NOTE = {Graduate Texts in Mathematics, No. 52},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {1977},
     PAGES = {xvi+496},
      ISBN = {0-387-90244-9},
   MRCLASS = {14-01},
  MRNUMBER = {0463157 (57 \#3116)},
MRREVIEWER = {Robert Speiser},
}

@incollection {Has,
    AUTHOR = {Hassett, B.},
     TITLE = {Equations of universal torsors and {C}ox rings},
 BOOKTITLE = {Mathematisches Institut, Georg-August-Universit\"at
              G\"ottingen: Seminars Summer Term 2004},
     PAGES = {135--143},
 PUBLISHER = {Universit\"atsdrucke G\"ottingen, G\"ottingen},
      YEAR = {2004},
   MRCLASS = {14J40 (14C22 14J26 14J45)},
  MRNUMBER = {2183138 (2007a:14046)},
MRREVIEWER = {Yuri Tschinkel},
}


@incollection {HaTs,
    AUTHOR = {Hassett, B. and Tschinkel, Y.},
     TITLE = {Universal torsors and {C}ox rings},
 BOOKTITLE = {Arithmetic of higher-dimensional algebraic varieties (Palo
              Alto, CA, 2002)},
    SERIES = {Progr. Math.},
    VOLUME = {226},
     PAGES = {149--173},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {2004},
   MRCLASS = {14J26 (14C20 14G27 14M25)},
  MRNUMBER = {2029868 (2005a:14049)},
MRREVIEWER = {Oleg N. Popov},
}


	
@inproceedings {HB,
    AUTHOR = {Heath-Brown, D. R.},
     TITLE = {The density of rational points on {C}ayley's cubic surface},
 BOOKTITLE = {Proceedings of the Session in Analytic Number Theory and
              Diophantine Equations},
    SERIES = {Bonner Math. Schriften},
    VOLUME = {360},
     PAGES = {33},
 PUBLISHER = {Univ. Bonn},
   ADDRESS = {Bonn},
      YEAR = {2003},
   MRCLASS = {14G05 (11G35 11G50)},
  MRNUMBER = {2075628 (2005d:14033)},
MRREVIEWER = {Yuri Tschinkel},
}

@article {HBM,
    AUTHOR = {Heath-Brown, D. R. and Moroz, B. Z.},
     TITLE = {The density of rational points on the cubic surface {$X\sb
              0\sp 3=X\sb 1X\sb 2X\sb 3$}},
   JOURNAL = {Math. Proc. Cambridge Philos. Soc.},
  FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical
              Society},
    VOLUME = {125},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {385--395},
      ISSN = {0305-0041},
     CODEN = {MPCPCO},
   MRCLASS = {11G50 (11P55 14G05)},
  MRNUMBER = {1656797 (2000f:11080)},
MRREVIEWER = {Carlo Gasbarri},
}
	
	


@article {Isk,
    AUTHOR = {Iskovskih, V. A.},
     TITLE = {Minimal models of rational surfaces over arbitrary fields},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {43},
      YEAR = {1979},
    NUMBER = {1},
     PAGES = {19--43, 237},
      ISSN = {0373-2436},
      NOTE = {English translation: Math. USSR-Izv. 14 (1980), no. 1, 17--39.},
   MRCLASS = {14J10 (14M20)},
  MRNUMBER = {525940 (80m:14021)},
MRREVIEWER = {Miles Reid},
}


@article {KeHu,
    AUTHOR = {Hu, Y. and Keel, S.},
     TITLE = {Mori dream spaces and {GIT}},
      NOTE = {Dedicated to William Fulton on the occasion of his 60th
              birthday},
   JOURNAL = {Michigan Math. J.},
  FJOURNAL = {The Michigan Mathematical Journal},
    VOLUME = {48},
      YEAR = {2000},
     PAGES = {331--348},
      ISSN = {0026-2285},
   MRCLASS = {14L24 (14E30)},
  MRNUMBER = {1786494 (2001i:14059)},
MRREVIEWER = {P. E. Newstead},
}
	
@book {Kol,
    AUTHOR = {Koll{\'a}r, J.},
     TITLE = {Rational curves on algebraic varieties},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A
              Series of Modern Surveys in Mathematics},
    VOLUME = {32},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1996},
     PAGES = {viii+320},
      ISBN = {3-540-60168-6},
   MRCLASS = {14-02 (14C05 14E05 14F17 14J45)},
  MRNUMBER = {1440180 (98c:14001)},
MRREVIEWER = {Yuri G. Prokhorov},
}



@book {KM,
    AUTHOR = {Koll{\'a}r, J. and Mori, S.},
     TITLE = {Birational geometry of algebraic varieties},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {134},
      NOTE = {With the collaboration of C. H. Clemens and A. Corti,
              Translated from the 1998 Japanese original},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {1998},
     PAGES = {viii+254},
      ISBN = {0-521-63277-3},
   MRCLASS = {14E30},
  MRNUMBER = {1658959 (2000b:14018)},
MRREVIEWER = {Mark Gross},
}

@book {lang,
    AUTHOR = {Lang, S.},
     TITLE = {Abelian varieties},
    SERIES = {Interscience Tracts in Pure and Applied Mathematics. No. 7},
 PUBLISHER = {Interscience Publishers, Inc., New York},
      YEAR = {1959},
     PAGES = {xii+256},
   MRCLASS = {14.00},
  MRNUMBER = {0106225 (21 \#4959)},
MRREVIEWER = {T. Matsusaka},
}

@misc {LV,
    AUTHOR = {A. Laface and M. Velasco},
     TITLE = {{P}icard-graded {B}etti numbers and the defining ideals of {C}ox rings},
      YEAR = {2007},
      NOTE = {arXiv:0707.3251},
}



		

@book {Laz,
    AUTHOR = {Lazarsfeld, R.},
     TITLE = {Positivity in algebraic geometry. {I}},
    SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A
              Series of Modern Surveys in Mathematics},
    VOLUME = {48},
      NOTE = {Classical setting: line bundles and linear series},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2004},
     PAGES = {xviii+387},
      ISBN = {3-540-22533-1},
   MRCLASS = {14-02 (14C20)},
  MRNUMBER = {2095471 (2005k:14001a)},
MRREVIEWER = {Mihnea Popa},
}





@book {Manin,
    AUTHOR = {Manin, Yu. I.},
     TITLE = {Cubic forms: algebra, geometry, arithmetic},
      NOTE = {Translated from Russian by M. Hazewinkel,
              North-Holland Mathematical Library, Vol. 4},
 PUBLISHER = {North-Holland Publishing Co.},
   ADDRESS = {Amsterdam},
      YEAR = {1974},
     PAGES = {vii+292},
      ISBN = {0-7204-2456-9},
   MRCLASS = {14M20 (14G25 10B15)},
  MRNUMBER = {0460349 (57 \#343)},
}

@article {Manin2,
    AUTHOR = {Manin, Yu. I.},
     TITLE = {Rational surfaces over perfect fields},
   JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.},
  FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications
              Math\'ematiques},
    NUMBER = {30},
      YEAR = {1966},
     PAGES = {55--113},
      ISSN = {0073-8301},
   MRCLASS = {14.20},
     NOTE  = {English translation:  American {M}athematical {S}ociety {T}ranslations. {S}eries 2,
              {V}ol. 84 (1969): {T}welve papers on algebra, algebraic geometry and
              topology},
  MRNUMBER = {0225780 (37 \#1373)},
MRREVIEWER = {M. L. Laplaza},
}


@article {MT,
    AUTHOR = {Manin, Yu. I. and Tsfasman, M. A.},
     TITLE = {Rational varieties: algebra, geometry, arithmetic},
   JOURNAL = {Uspekhi Mat. Nauk},
  FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo.
              Uspekhi Matematicheskikh Nauk},
    VOLUME = {41},
      YEAR = {1986},
    NUMBER = {2(248)},
     PAGES = {43--94},
      ISSN = {0042-1316},
   MRCLASS = {11G35 (14G05 14J20)},
     NOTE  = {English translation: Russian Math. Surveys 41 (1986), no. 2, 51--116},
  MRNUMBER = {842161 (87k:11065)},
MRREVIEWER = {Daniel Coray},
}


@book {Mat,
    AUTHOR = {Matsuki, K.},
     TITLE = {Introduction to the {M}ori program},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {New York},
      YEAR = {2002},
     PAGES = {xxiv+478},
      ISBN = {0-387-98465-8},
   MRCLASS = {14E30 (14-02 14E05 14J17 14J30)},
  MRNUMBER = {1875410 (2002m:14011)},
MRREVIEWER = {Massimiliano Mella},
}
		


@book {Mil,
    AUTHOR = {Milne, J. S.},
     TITLE = {\'{E}tale cohomology},
    SERIES = {Princeton Mathematical Series},
    VOLUME = {33},
 PUBLISHER = {Princeton University Press},
   ADDRESS = {Princeton, N.J.},
      YEAR = {1980},
     PAGES = {xiii+323},
      ISBN = {0-691-08238-3},
   MRCLASS = {14-02 (14F20 18F99)},
  MRNUMBER = {559531 (81j:14002)},
MRREVIEWER = {G. Horrocks},
}

@book {MumCAG,
    AUTHOR = {Mumford, D.},
     TITLE = {Algebraic geometry. {I}},
    SERIES = {Classics in Mathematics},
      NOTE = {Complex projective varieties,
              Reprint of the 1976 edition},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1995},
     PAGES = {x+186},
      ISBN = {3-540-58657-1},
   MRCLASS = {14-XX},
  MRNUMBER = {1344216 (96d:14001)},
}




@incollection {polymake,
    AUTHOR = {Gawrilow, E. and Joswig, M.},
     TITLE = {polymake: a framework for analyzing convex polytopes},
 BOOKTITLE = {Polytopes---combinatorics and computation ({O}berwolfach,
              1997)},
  EDITOR =   {G. Kalai and G.M. Ziegler},
    SERIES = {DMV Sem.},
    VOLUME = {29},
     PAGES = {43--73},
 PUBLISHER = {Birkh\"auser},
   ADDRESS = {Basel},
      YEAR = {2000},
   MRCLASS = {52B55 (68U05)},
  MRNUMBER = {1785292 (2001f:52033)},
     NOTE = {software available at  \texttt{
	http://www.math.tu-berlin.de/polymake/}},
}
	
	
@misc {PORTA,
  AUTHOR = {T. Christof and  A. L\"obel},
   TITLE = { Polyhedron representation transformation algorithm ({PORTA})},
    YEAR = {1997},
    NOTE = {software available at
\texttt{http://www.iwr.uni-heidelberg.de/groups/ comopt/software/PORTA}},
}




@incollection {Reid,
    AUTHOR = {Reid, M.},
     TITLE = {Chapters on algebraic surfaces},
 BOOKTITLE = {Complex algebraic geometry (Park City, UT, 1993)},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {3},
     PAGES = {3--159},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1997},
   MRCLASS = {14J10 (14J17 14J25)},
  MRNUMBER = {1442522 (98d:14049)},
MRREVIEWER = {Mark Gross},
}

@misc {Po,
   AUTHOR = {O. N. Popov},
    TITLE = {{D}el {P}ezzo surfaces and algebraic groups}, 
    NOTE = {Diplomarbeit, Universit\"at T\"ubingen},
     YEAR = {2001},
}


@article {Sal,
    AUTHOR = {Salberger, P.},
     TITLE = {Tamagawa measures on universal torsors and points of bounded
              height on {F}ano varieties},
      NOTE = {Nombre et r\'epartition de points de hauteur born\'ee (Paris,
              1996)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {251},
      YEAR = {1998},
     PAGES = {91--258},
      ISSN = {0303-1179},
   MRCLASS = {11G50 (11G35 14G05 14G25 14J45)},
  MRNUMBER = {1679841 (2000d:11091)},
MRREVIEWER = {David Harari},
}

@article {SB,
    AUTHOR = {Shepherd-Barron, N. I.},
     TITLE = {On simple groups and simple singularities},
   JOURNAL = {Israel J. Math.},
  FJOURNAL = {Israel Journal of Mathematics},
    VOLUME = {123},
      YEAR = {2001},
     PAGES = {179--188},
      ISSN = {0021-2172},
     CODEN = {ISJMAP},
   MRCLASS = {14L30 (14B07 14B12 14J17)},
  MRNUMBER = {1835294 (2002c:14076)},
MRREVIEWER = {Dmitrii A. Timash{\"e}v},
}
	
@article {SeSk,
    AUTHOR = {Serganova, V. V. and Skorobogatov, A. N.},
     TITLE = {Del {P}ezzo surfaces and representation theory},
   JOURNAL = {Algebra Number Theory},
  FJOURNAL = {Algebra \& Number Theory},
    VOLUME = {1},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {393--419},
      ISSN = {1937-0652},
   MRCLASS = {14J26 (17B10 17B25)},
  MRNUMBER = {2368955},
}

@article {Sh,
    AUTHOR = {Shokurov, V. V.},
     TITLE = {{$3$}-fold log models},
      NOTE = {Algebraic geometry, 4},
   JOURNAL = {J. Math. Sci.},
  FJOURNAL = {Journal of Mathematical Sciences},
    VOLUME = {81},
      YEAR = {1996},
    NUMBER = {3},
     PAGES = {2667--2699},
      ISSN = {1072-3374},
     CODEN = {JMTSEW},
   MRCLASS = {14E30 (14E15 14E35)},
  MRNUMBER = {1420223 (97i:14015)},
MRREVIEWER = {Alessio Corti},
}


@article {Sk,
    AUTHOR = {Skorobogatov, A. N.},
     TITLE = {On a theorem of {E}nriques-{S}winnerton-{D}yer},
   JOURNAL = {Ann. Fac. Sci. Toulouse Math. (6)},
  FJOURNAL = {Toulouse. Facult\'e des Sciences. Annales. Math\'ematiques.
              S\'erie 6},
    VOLUME = {2},
      YEAR = {1993},
    NUMBER = {3},
     PAGES = {429--440},
      ISSN = {0240-2955},
   MRCLASS = {14G05 (14J26 14M15)},
  MRNUMBER = {1260765 (95b:14018)},
MRREVIEWER = {P. Abellanas},
}


@book {Skbook,
    AUTHOR = {Skorobogatov, A. N.},
     TITLE = {Torsors and rational points},
    SERIES = {Cambridge Tracts in Mathematics},
    VOLUME = {144},
 PUBLISHER = {Cambridge University Press},
   ADDRESS = {Cambridge},
      YEAR = {2001},
     PAGES = {viii+187},
      ISBN = {0-521-80237-7},
   MRCLASS = {14G05 (11G35 11S25 14D10 14G25 14L30)},
  MRNUMBER = {1845760 (2002d:14032)},
MRREVIEWER = {Tam{\'a}s Szamuely},
}

@article {STV,
	AUTHOR = {M. Stillman and D. Testa and M. Velasco},
         TITLE = {{G}r\"obner bases, monomial group actions,
		and the {C}ox rings of del {P}ezzo surfaces},
        JOURNAL = {J. Algebra},
       FJOURNAL = {Journal of Algebra},
        VOLUME = {316},
        YEAR = {2007},
	NUMBER = {2},
     	PAGES = {777--801},
      ISSN = {0021-8693},
	MRNUMBER = {2358614 (2008i:14054)},
}

@misc {SX,
	AUTHOR = {B. Sturmfels and  Z. Xu},
         TITLE = {Sagbi Bases of {C}ox-{N}agata Rings},
          YEAR = {2008},
          NOTE = {arXiv:0803.0892},
}


@incollection {SwD,
    AUTHOR = {Swinnerton-Dyer, H. P. F.},
     TITLE = {Rational points on del {P}ezzo surfaces of degree {$5$}},
 BOOKTITLE = {Algebraic geometry, Oslo 1970 (Proc. Fifth Nordic Summer
              School in Math.)},
     PAGES = {287--290},
 PUBLISHER = {Wolters-Noordhoff},
   ADDRESS = {Groningen},
      YEAR = {1972},
   MRCLASS = {14G05 (14J25)},
  MRNUMBER = {0376684 (51 \#12859)},
MRREVIEWER = {M. Fried},
}

@misc {TVAV,
   AUTHOR = {D. Testa and A. V\'arilly-Alvarado and M. Velasco},
   TITLE = {Cox rings of degree one del {P}ezzo surfaces},
   YEAR = {2008},
   NOTE = {arXiv:0803.0353},
}

@article {Zar1,
    AUTHOR = {Zariski, O.},
     TITLE = {On {C}astelnuovo's criterion of rationality
              {$p\sb{a}=P\sb{2}=0$} of an algebraic surface},
   JOURNAL = {Illinois J. Math.},
  FJOURNAL = {Illinois Journal of Mathematics},
    VOLUME = {2},
      YEAR = {1958},
     PAGES = {303--315},
      ISSN = {0019-2082},
   MRCLASS = {14.00},
  MRNUMBER = {0099990 (20 \#6426)},
MRREVIEWER = {J. Guerindon},
}

@article {Zar2,
    AUTHOR = {Zariski, O.},
     TITLE = {The problem of minimal models in the theory of algebraic
              surfaces},
   JOURNAL = {Amer. J. Math.},
  FJOURNAL = {American Journal of Mathematics},
    VOLUME = {80},
      YEAR = {1958},
     PAGES = {146--184},
      ISSN = {0002-9327},
   MRCLASS = {14.00},
  MRNUMBER = {0097404 (20 \#3873)},
MRREVIEWER = {M. Nagata},
}

@article {Zar3,
    AUTHOR = {Zariski, O.},
     TITLE = {The theorem of {R}iemann-{R}och for high multiples of an
              effective divisor on an algebraic surface},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {76},
      YEAR = {1962},
     PAGES = {560--615},
      ISSN = {0003-486X},
   MRCLASS = {14.20 (14.15)},
  MRNUMBER = {0141668 (25 \#5065)},
MRREVIEWER = {Y. Nakai},
}