\begin{thebibliography}{KMM92b}

\bibitem[AK77]{AK}
Allen~B. Altman and Steven~L. Kleiman.
\newblock Foundations of the theory of {F}ano schemes.
\newblock {\em Compositio Math.}, 34(1):3--47, 1977.

\bibitem[Art69]{Art69}
Michael Artin.
\newblock Algebraization of formal moduli. {I}.
\newblock In {\em Global {A}nalysis ({P}apers in {H}onor of {K}. {K}odaira)},
  pages 21--71. Univ. Tokyo Press, Tokyo, 1969.

\bibitem[AV02]{AV}
Dan Abramovich and Angelo Vistoli.
\newblock Compactifying the space of stable maps.
\newblock {\em J. Amer. Math. Soc.}, 15(1):27--75 (electronic), 2002.

\bibitem[BM96]{BM}
Kai Behrend and Yuri Manin.
\newblock Stacks of stable maps and {G}romov-{W}itten invariants.
\newblock {\em Duke Math. J.}, 85(1):1--60, 1996.

\bibitem[Bri66]{Bries}
Egbert Brieskorn.
\newblock \"{U}ber die {A}ufl\"osung gewisser {S}ingularit\"aten von
  holomorphen {A}bbildungen.
\newblock {\em Math. Ann.}, 166:76--102, 1966.

\bibitem[Cam92]{Cam}
Fr\'ed\'eric Campana.
\newblock Connexit\'e rationnelle des vari\'et\'es de {F}ano.
\newblock {\em Ann. Sci. \'Ecole Norm. Sup. (4)}, 25(5):539--545, 1992.

\bibitem[Cor96]{Cor}
Alessio Corti.
\newblock Del {P}ezzo surfaces over {D}edekind schemes.
\newblock {\em Ann. of Math. (2)}, 144(3):641--683, 1996.

\bibitem[CTG04]{CTG}
Jean-Louis Colliot-Th{\'e}l{\`e}ne and Philippe Gille.
\newblock Remarques sur l'approximation faible sur un corps de fonctions d'une
  variable.
\newblock In {\em Arithmetic of higher-dimensional algebraic varieties ({P}alo
  {A}lto, {CA}, 2002)}, volume 226 of {\em Progr. Math.}, pages 121--134.
  Birkh\"auser Boston, Boston, MA, 2004.

\bibitem[Deb01]{Debbook}
Olivier Debarre.
\newblock {\em Higher-dimensional algebraic geometry}.
\newblock Universitext. Springer-Verlag, New York, 2001.

\bibitem[Deb03]{DebBour}
Olivier Debarre.
\newblock Vari\'et\'es rationnellement connexes (d'apr\`es {T}. {G}raber, {J}.
  {H}arris, {J}. {S}tarr et {A}. {J}. de {J}ong).
\newblock {\em Ast\'erisque}, 290:Exp. No. 905, ix, 243--266, 2003.
\newblock S\'eminaire Bourbaki. Vol. 2001/2002.

\bibitem[dJS06]{dJS}
A.~J. de~Jong and Jason Starr.
\newblock Low degree complete intersections are rationally simply connected,
  2006.
\newblock available at
  \texttt{http://www.math.sunysb.edu/$\sim$jstarr/papers/index.html}.

\bibitem[FP97]{FP}
William Fulton and Rahul Pandharipande.
\newblock Notes on stable maps and quantum cohomology.
\newblock In {\em Algebraic geometry---Santa Cruz 1995}, volume~62 of {\em
  Proc. Sympos. Pure Math.}, pages 45--96. Amer. Math. Soc., Providence, RI,
  1997.

\bibitem[GHS03]{GHS}
Tom Graber, Joe Harris, and Jason Starr.
\newblock Families of rationally connected varieties.
\newblock {\em J. Amer. Math. Soc.}, 16(1):57--67 (electronic), 2003.

\bibitem[GM88]{GM}
Mark Goresky and Robert MacPherson.
\newblock {\em Stratified {M}orse theory}, volume~14 of {\em Ergebnisse der
  Mathematik und ihrer Grenzgebiete (3)}.
\newblock Springer-Verlag, Berlin, 1988.

\bibitem[Har68]{Harder}
G{\"u}nter Harder.
\newblock Eine {B}emerkung zum schwachen {A}pproximationssatz.
\newblock {\em Arch. Math. (Basel)}, 19:465--471, 1968.

\bibitem[Har79]{Har79}
Joe Harris.
\newblock Galois groups of enumerative problems.
\newblock {\em Duke Math. J.}, 46(4):685--724, 1979.

\bibitem[Har04]{Harari}
David Harari.
\newblock Weak approximation on algebraic varieties.
\newblock In {\em Arithmetic of higher-dimensional algebraic varieties ({P}alo
  {A}lto, {CA}, 2002)}, volume 226 of {\em Progr. Math.}, pages 43--60.
  Birkh\"auser Boston, Boston, MA, 2004.

\bibitem[Has03]{Ha}
Brendan Hassett.
\newblock Moduli spaces of weighted pointed stable curves.
\newblock {\em Adv. Math.}, 173(2):316--352, 2003.

\bibitem[Has09]{HaCMI}
Brendan Hassett.
\newblock Rational surfaces over nonclosed fields.
\newblock In {\em Arithmetic Geometry}, volume~8 of {\em Clay Mathematics
  Proceedings}, pages 155--210, Providence, RI, 2009. Amer. Math. Soc.
\newblock 2006 Clay Mathematics Institute Summer School in G\"ottingen.

\bibitem[HT06]{HT06}
Brendan Hassett and Yuri Tschinkel.
\newblock Weak approximation over function fields.
\newblock {\em Invent. Math.}, 163(1):171--190, 2006.

\bibitem[HT08a]{HT08}
Brendan Hassett and Yuri Tschinkel.
\newblock Approximation at places of bad reduction for rationally connected
  varieties.
\newblock {\em Pure Appl. Math. Q.}, 4(3):743--766, 2008.

\bibitem[HT08b]{HT08b}
Brendan Hassett and Yuri Tschinkel.
\newblock Log {F}ano varieties over function fields of curves.
\newblock {\em Invent. Math.}, 173(1):7--21, 2008.

\bibitem[HT09]{HT09}
Brendan Hassett and Yuri Tschinkel.
\newblock Weak approximation for hypersurfaces of low degree.
\newblock In {\em Algebraic geometry---{S}eattle 2005. {P}art 2}, volume~80 of
  {\em Proc. Sympos. Pure Math.}, pages 937--955. Amer. Math. Soc., Providence,
  RI, 2009.

\bibitem[Isk79]{Isk}
Vasilii~A. Iskovskikh.
\newblock Minimal models of rational surfaces over arbitrary fields.
\newblock {\em Izv. Akad. Nauk SSSR Ser. Mat.}, 43(1):19--43, 237, 1979.
\newblock English translation: Math. USSR-Izv. {\bf 14} (1980), no. 1, 17--39.

\bibitem[KM94]{KM}
Maxim Kontsevich and Yuri Manin.
\newblock Gromov-{W}itten classes, quantum cohomology, and enumerative
  geometry.
\newblock {\em Comm. Math. Phys.}, 164(3):525--562, 1994.

\bibitem[KMM92a]{KMMb}
J{\'a}nos Koll{\'a}r, Yoichi Miyaoka, and Shigefumi Mori.
\newblock Rational connectedness and boundedness of {F}ano manifolds.
\newblock {\em J. Differential Geom.}, 36(3):765--779, 1992.

\bibitem[KMM92b]{KMM}
J{\'a}nos Koll{\'a}r, Yoichi Miyaoka, and Shigefumi Mori.
\newblock Rationally connected varieties.
\newblock {\em J. Algebraic Geom.}, 1(3):429--448, 1992.

\bibitem[Kne62]{Kneser2}
Martin Kneser.
\newblock Schwache {A}pproximation in algebraischen {G}ruppen.
\newblock In {\em Colloq. {T}h\'eorie des {G}roupes {A}lg\'ebriques
  ({B}ruxelles, 1962)}, pages 41--52. Librairie Universitaire, Louvain, 1962.

\bibitem[Kne07]{Kn1}
Amanda Knecht.
\newblock {\em Weak Approximation for Degree 2 del {P}ezzo Surfaces at Places
  of Bad Reduction}.
\newblock PhD thesis, Rice University, 2007.

\bibitem[Kne08]{Kn2}
Amanda Knecht.
\newblock Weak approximation for general degree two del {P}ezzo surfaces, 2008.
\newblock arXiv:0809.1251v1.

\bibitem[Knu83]{KnMu}
Finn~F. Knudsen.
\newblock The projectivity of the moduli space of stable curves. {II}. {T}he
  stacks {$M\sb{g,n}$}.
\newblock {\em Math. Scand.}, 52(2):161--199, 1983.

\bibitem[Kol96]{Kolbook}
J{\'a}nos Koll{\'a}r.
\newblock {\em Rational curves on algebraic varieties}, volume~32 of {\em
  Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge.}
\newblock Springer-Verlag, Berlin, 1996.

\bibitem[Kon95]{K}
Maxim Kontsevich.
\newblock Enumeration of rational curves via torus actions.
\newblock In {\em The moduli space of curves (Texel Island, 1994)}, volume 129
  of {\em Progr. Math.}, pages 335--368. Birkh\"auser Boston, Boston, MA, 1995.

\bibitem[LMB00]{LMB}
G{\'e}rard Laumon and Laurent Moret-Bailly.
\newblock {\em Champs alg\'ebriques}, volume~39 of {\em Ergebnisse der
  Mathematik und ihrer Grenzgebiete. 3. Folge.}
\newblock Springer-Verlag, Berlin, 2000.

\bibitem[Man66]{Manin}
Yuri~I. Manin.
\newblock Rational surfaces over perfect fields.
\newblock {\em Inst. Hautes \'Etudes Sci. Publ. Math.}, 30:55--113, 1966.

\bibitem[Man86]{Maninbook}
Yuri~I. Manin.
\newblock {\em Cubic forms: {A}lgebra, geometry, arithmetic}, volume~4 of {\em
  North-Holland Mathematical Library}.
\newblock North-Holland Publishing Co., Amsterdam, second edition, 1986.
\newblock Translated from the Russian by M. Hazewinkel.

\bibitem[Pir09]{Pirutka}
Alena Pirutka.
\newblock {R}-equivalence on low degree complete intersections, 2009.
\newblock arXiv:math/0907.1971v2.

\bibitem[Ser73]{Se}
Jean-Pierre Serre.
\newblock {\em A course in arithmetic}.
\newblock Springer-Verlag, New York, 1973.
\newblock Translated from the French, Graduate Texts in Mathematics, No. 7.

\bibitem[Sta06]{Starr06}
Jason Starr.
\newblock Hypersurfaces of low degree are rationally simply-connected, 2006.
\newblock arXiv:math/0602641v1.

\bibitem[Sta09]{StarrClay}
Jason Starr.
\newblock Arithmetic over function fields.
\newblock In {\em Arithmetic Geometry}, volume~8 of {\em Clay Mathematics
  Proceedings}, pages 375--418, Providence, RI, 2009. Amer. Math. Soc.
\newblock 2006 Clay Mathematics Institute Summer School in G\"ottingen.

\bibitem[Tei75]{Te}
Bernard Teissier.
\newblock Introduction to equisingularity problems.
\newblock In {\em Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29,
  Humboldt State Univ., Arcata, Calif., 1974)}, pages 593--632. Amer. Math.
  Soc., Providence, R.I., 1975.

\bibitem[Xu09a]{Xu}
Chenyang Xu.
\newblock Strong rational connectedness of surfaces, 2009.
\newblock arXiv:0810.2597v3.

\bibitem[Xu09b]{Xu2}
Chenyang Xu.
\newblock Weak approximation for low degree del {P}ezzo surfaces, 2009.
\newblock arXiv:0902.1765.

\end{thebibliography}
