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D.~Abramovich.
\newblock Birational geometry for number theorists.
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C.~Birkar, P.~Cascini, Chr.~D. Hacon, and James McKernan.
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\bibitem[BDPP13]{BDPP}
S{\'e}bastien Boucksom, Jean-Pierre Demailly, Mihai Paun, and Thomas Peternell.
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\newblock {\em J. Algebraic Geom.}, 22(2):201--248, 2013.

\bibitem[Beh06]{Be06}
Roya Beheshti.
\newblock Lines on projective hypersurfaces.
\newblock {\em J. Reine Angew. Math.}, 592:1--21, 2006.

\bibitem[BFJ09]{BFJ}
S{\'e}bastien Boucksom, Charles Favre, and Mattias Jonsson.
\newblock Differentiability of volumes of divisors and a problem of {T}eissier.
\newblock {\em J. Algebraic Geom.}, 18(2):279--308, 2009.

\bibitem[BM90]{BM}
V.~V. Batyrev and Yu.~I. Manin.
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\bibitem[Bor91]{LAG}
Armand Borel.
\newblock {\em Linear algebraic groups}, volume 126 of {\em Graduate Texts in
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\newblock Springer-Verlag, New York, second edition, 1991.

\bibitem[Bou04]{B04}
S{\'e}bastien Boucksom.
\newblock Divisorial {Z}ariski decompositions on compact complex manifolds.
\newblock {\em Ann. Sci. \'Ecole Norm. Sup. (4)}, 37(1):45--76, 2004.

\bibitem[BT95]{BT-IMRN}
Victor~V. Batyrev and Yuri Tschinkel.
\newblock Rational points of bounded height on compactifications of anisotropic
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\newblock {\em Internat. Math. Res. Notices}, (12):591--635, 1995.

\bibitem[BT96a]{BT-general}
V.~Batyrev and Yu. Tschinkel.
\newblock Height zeta functions of toric varieties.
\newblock {\em J. Math. Sci.}, 82(1):3220--3239, 1996.
\newblock Algebraic geometry, 5.

\bibitem[BT96b]{BT-cubic}
V.~V. Batyrev and Y.~Tschinkel.
\newblock Rational points on some {F}ano cubic bundles.
\newblock {\em C. R. Acad. Sci. Paris S\'er. I Math.}, 323(1):41--46, 1996.

\bibitem[BT98a]{BT-0}
V.~V. Batyrev and Y.~Tschinkel.
\newblock Manin's conjecture for toric varieties.
\newblock {\em J. Algebraic Geom.}, 7(1):15--53, 1998.

\bibitem[BT98b]{BT}
V.~V. Batyrev and Y.~Tschinkel.
\newblock Tamagawa numbers of polarized algebraic varieties.
\newblock {\em Ast\'erisque}, (251):299--340, 1998.
\newblock Nombre et r\'epartition de points de hauteur born\'ee (Paris, 1996).

\bibitem[BT99]{bog-t}
F.~A. Bogomolov and Yu. Tschinkel.
\newblock On the density of rational points on elliptic fibrations.
\newblock {\em J. Reine Angew. Math.}, 511:87--93, 1999.

\bibitem[Cam04]{campana}
F.~Campana.
\newblock Orbifolds, special varieties and classification theory.
\newblock {\em Ann. Inst. Fourier (Grenoble)}, 54(3):499--630, 2004.

\bibitem[CLT02]{chambert-t02}
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\newblock On the distribution of points of bounded height on equivariant
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\bibitem[Cut86]{Cut86}
Steven~D. Cutkosky.
\newblock Zariski decomposition of divisors on algebraic varieties.
\newblock {\em Duke Math. J.}, 53(1):149--156, 1986.

\bibitem[DC12]{DiCerbo}
Gabriele Di~Cerbo.
\newblock On {F}ujita's log spectrum conjecture, 2012.
\newblock {\tt arXiv:1210.5234}.

\bibitem[Deb03]{Debarre}
Olivier Debarre.
\newblock Lines on smooth hypersurfaces, 2003.
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\bibitem[FMT89]{FMT}
J.~Franke, Y.~I. Manin, and Y.~Tschinkel.
\newblock Rational points of bounded height on {F}ano varieties.
\newblock {\em Invent. Math.}, 95(2):421--435, 1989.

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\newblock Introduction to the toric {M}ori theory.
\newblock {\em Michigan Math. J.}, 52(3):649--665, 2004.

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T.~Fujita.
\newblock On polarized manifolds whose adjoint bundles are not semipositive.
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T.~Fujita.
\newblock On {K}odaira energy and adjoint reduction of polarized manifolds.
\newblock {\em Manuscripta Math.}, 76(1):59--84, 1992.

\bibitem[Fuj96]{fujita-log}
T.~Fujita.
\newblock On {K}odaira energy of polarized log varieties.
\newblock {\em J. Math. Soc. Japan}, 48(1):1--12, 1996.

\bibitem[Fuj97]{fujita-three}
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\newblock On {K}odaira energy and adjoint reduction of polarized threefolds.
\newblock {\em Manuscripta Math.}, 94(2):211--229, 1997.

\bibitem[FZ13]{FuZhang}
Baohua Fu and De-Qi Zhang.
\newblock A characterization of compact complex tori via automorphism groups.
\newblock {\em Math. Ann.}, 2013.

\bibitem[GH78]{GH}
Phillip Griffiths and Joseph Harris.
\newblock {\em Principles of algebraic geometry}.
\newblock Wiley-Interscience [John Wiley \& Sons], New York, 1978.
\newblock Pure and Applied Mathematics.

\bibitem[GTBT11]{goro-ramin-t}
A.~Gorodnik, R.~Takloo-Bighash, and Y.~Tschinkel.
\newblock Multiple mixing for adele groups and rational points, 2011.
\newblock {\tt arXiv:1112.5743}.

\bibitem[HK00]{MDS}
Yi~Hu and Sean Keel.
\newblock Mori dream spaces and {GIT}.
\newblock {\em Michigan Math. J.}, 48:331--348, 2000.
\newblock Dedicated to William Fulton on the occasion of his 60th birthday.

\bibitem[HT99]{HT}
B.~Hassett and Y.~Tschinkel.
\newblock Geometry of equivariant compactifications of {${\bf G}_a^n$}.
\newblock {\em Internat. Math. Res. Notices}, (22):1211--1230, 1999.

\bibitem[HT00a]{Harris-T}
J.~Harris and Y.~Tschinkel.
\newblock Rational points on quartics.
\newblock {\em Duke Math. J.}, 104(3):477--500, 2000.

\bibitem[HT00b]{HT00}
Brendan Hassett and Yuri Tschinkel.
\newblock Abelian fibrations and rational points on symmetric products.
\newblock {\em Internat. J. Math.}, 11(9):1163--1176, 2000.

\bibitem[KKLV89]{KKLV89}
Friedrich Knop, Hanspeter Kraft, Domingo Luna, and Thierry Vust.
\newblock Local properties of algebraic group actions.
\newblock In {\em Algebraische {T}ransformationsgruppen und
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\bibitem[KKV89]{KKV}
Friedrich Knop, Hanspeter Kraft, and Thierry Vust.
\newblock The {P}icard group of a {$G$}-variety.
\newblock In {\em Algebraische {T}ransformationsgruppen und
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\bibitem[KMM87]{KMM87}
Yujiro Kawamata, Katsumi Matsuda, and Kenji Matsuki.
\newblock Introduction to the minimal model problem.
\newblock In {\em Algebraic geometry, {S}endai, 1985}, volume~10 of {\em Adv.
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\bibitem[KMM92]{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[Laz04a]{LazI}
Robert Lazarsfeld.
\newblock {\em Positivity in algebraic geometry. {I}}, volume~48 of {\em
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\newblock Springer-Verlag, Berlin, 2004.
\newblock Classical setting: line bundles and linear series.

\bibitem[Laz04b]{LazII}
Robert Lazarsfeld.
\newblock {\em Positivity in algebraic geometry. {II}}, volume~49 of {\em
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\newblock Springer-Verlag, Berlin, 2004.
\newblock Positivity for vector bundles, and multiplier ideals.

\bibitem[Leh12]{L11}
Brian Lehmann.
\newblock A cone theorem for nef curves.
\newblock {\em J. Algebraic Geom.}, 21(3):473--493, 2012.

\bibitem[Leh13]{L11B}
Brian Lehmann.
\newblock Comparing numerical dimensions.
\newblock {\em Algebra Number Theory}, 7(5):1065--1100, 2013.

\bibitem[Leh14]{L14}
Brian Lehmann.
\newblock On {E}ckl's pseudo-effective reduction map.
\newblock {\em Trans. Amer. Math. Soc.}, 366(3):1525--1549, 2014.

\bibitem[LT10]{LT10}
J.~M. Landsberg and Orsola Tommasi.
\newblock On the {D}ebarre-de {J}ong and {B}eheshti-{S}tarr conjectures on
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\newblock {\em Michigan Math. J.}, 59(3):573--588, 2010.

\bibitem[MFK94]{GIT}
D.~Mumford, J.~Fogarty, and F.~Kirwan.
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\bibitem[MU83]{MU83}
Shigeru Mukai and Hiroshi Umemura.
\newblock Minimal rational threefolds.
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\bibitem[Nak04]{Nak}
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\newblock {\em Zariski-decomposition and abundance}, volume~14 of {\em MSJ
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\newblock Mathematical Society of Japan, Tokyo, 2004.

\bibitem[Pet12]{Peternell12}
Thomas Peternell.
\newblock Varieties with generically nef tangent bundles.
\newblock {\em J. Eur. Math. Soc. (JEMS)}, 14(2):571--603, 2012.

\bibitem[Pey95]{peyre}
E.~Peyre.
\newblock Hauteurs et mesures de {T}amagawa sur les vari\'et\'es de {F}ano.
\newblock {\em Duke Math. J.}, 79(1):101--218, 1995.

\bibitem[Som86]{sommese}
A.~J. Sommese.
\newblock On the adjunction theoretic structure of projective varieties.
\newblock In {\em Complex analysis and algebraic geometry ({G}\"ottingen,
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\bibitem[Tsc09]{T}
Y.~Tschinkel.
\newblock Algebraic varieties with many rational points.
\newblock In {\em Arithmetic geometry}, volume~8 of {\em Clay Math. Proc.},
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