Existence of minimal models for varieties of log general type
Journal of the American Mathematical Society, Tome 23 (2010) no. 2, pp. 405-468

Voir la notice de l'article provenant de la source American Mathematical Society

We prove that the canonical ring of a smooth projective variety is finitely generated.
DOI : 10.1090/S0894-0347-09-00649-3

Birkar, Caucher 1 ; Cascini, Paolo 2 ; Hacon, Christopher 3 ; McKernan, James 4

1 DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
2 Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106 and Imperial College London, 180 Queens Gate, London SW7 2A2, United Kingdom
3 Department of Mathematics, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112
4 Department of Mathematics, University of California at Santa Barbara, Santa Barbara, California 93106 and Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
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Birkar, Caucher; Cascini, Paolo; Hacon, Christopher; McKernan, James. Existence of minimal models for varieties of log general type. Journal of the American Mathematical Society, Tome 23 (2010) no. 2, pp. 405-468. doi: 10.1090/S0894-0347-09-00649-3

[1] Alexeev, Valery, Hacon, Christopher, Kawamata, Yujiro Termination of (many) 4-dimensional log flips Invent. Math. 2007 433 448

[2] Birkar, Caucher Ascending chain condition for log canonical thresholds and termination of log flips Duke Math. J. 2007 173 180

[3] Bump, Daniel Lie groups 2004

[4] Eyssidieux, Philippe, Guedj, Vincent, Zeriahi, Ahmed Singular Kähler-Einstein metrics J. Amer. Math. Soc. 2009 607 639

[5] Fujino, Osamu Termination of 4-fold canonical flips Publ. Res. Inst. Math. Sci. 2004 231 237

[6] Fujino, Osamu, Mori, Shigefumi A canonical bundle formula J. Differential Geom. 2000 167 188

[7] Gibney, Angela, Keel, Sean, Morrison, Ian Towards the ample cone of \overline𝑀_{𝑔,𝑛} J. Amer. Math. Soc. 2002 273 294

[8] Flips for 3-folds and 4-folds 2007

[9] Hartshorne, Robin Algebraic geometry 1977

[10] Hassett, Brendan, Hyeon, Donghoon Log canonical models for the moduli space of curves: the first divisorial contraction Trans. Amer. Math. Soc. 2009 4471 4489

[11] Hu, Yi, Keel, Sean Mori dream spaces and GIT Michigan Math. J. 2000 331 348

[12] Kawakita, Masayuki Inversion of adjunction on log canonicity Invent. Math. 2007 129 133

[13] Kawamata, Yujiro The Zariski decomposition of log-canonical divisors 1987 425 433

[14] Kawamata, Yujiro Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces Ann. of Math. (2) 1988 93 163

[15] Kawamata, Yujiro On the length of an extremal rational curve Invent. Math. 1991 609 611

[16] Kawamata, Yujiro Flops connect minimal models Publ. Res. Inst. Math. Sci. 2008 419 423

[17] Kawamata, Yujiro, Matsuda, Katsumi, Matsuki, Kenji Introduction to the minimal model problem 1987 283 360

[18] Kollã¡R, Jã¡Nos Flips, flops, minimal models, etc 1991 113 199

[19] Kollã¡R, Jã¡Nos Effective base point freeness Math. Ann. 1993 595 605

[20] Flips and abundance for algebraic threefolds 1992 1 258

[21] Kollã¡R, Jã¡Nos, Mori, Shigefumi Birational geometry of algebraic varieties 1998

[22] Lazarsfeld, Robert Positivity in algebraic geometry. II 2004

[23] Manin, Yuri Moduli stacks \overline𝐿_{𝑔,𝑆} Mosc. Math. J. 2004

[24] Matsuki, Kenji Termination of flops for 4-folds Amer. J. Math. 1991 835 859

[25] Mori, Shigefumi Flip theorem and the existence of minimal models for 3-folds J. Amer. Math. Soc. 1988 117 253

[26] Mumford, David Stability of projective varieties Enseign. Math. (2) 1977 39 110

[27] Nakayama, Noboru Zariski-decomposition and abundance 2004

[28] Nikulin, Viacheslav V. The diagram method for 3-folds and its application to the Kähler cone and Picard number of Calabi-Yau 3-folds. I 1996 261 328

[29] Peternell, Thomas Towards a Mori theory on compact Kähler threefolds. II Math. Ann. 1998 729 764

[30] Shokurov, V. V. Three-dimensional log perestroikas Izv. Ross. Akad. Nauk Ser. Mat. 1992 105 203

[31] Shokurov, V. V. 3-fold log models J. Math. Sci. 1996 2667 2699

[32] Shokurov, V. V. Letters of a bi-rationalist. I. A projectivity criterion 1997 143 152

[33] Shokurov, V. V. Prelimiting flips Tr. Mat. Inst. Steklova 2003 82 219

[34] Shokurov, V. V. Letters of a bi-rationalist. V. Minimal log discrepancies and termination of log flips Tr. Mat. Inst. Steklova 2004 328 351

[35] Ueno, Kenji Bimeromorphic geometry of algebraic and analytic threefolds 1982 1 34

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