Minimal model program for excellent surfaces
[Programme des modèles minimaux pour des surfaces excellentes]
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 345-376.

Nous prouvons les résultats prédits par le programme des modèles minimaux pour des surfaces log canoniques et Q-factorielles sur des schémas excellents.

We establish the minimal model program for log canonical and Q-factorial surfaces over excellent base schemes.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : https://doi.org/10.5802/aif.3163
Classification : 14E30
Mots clés : Modèles minimaux, surfaces excellentes, log canonique
@article{AIF_2018__68_1_345_0,
     author = {Tanaka, Hiromu},
     title = {Minimal model program for excellent surfaces},
     journal = {Annales de l'Institut Fourier},
     pages = {345--376},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {68},
     number = {1},
     year = {2018},
     doi = {10.5802/aif.3163},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/aif.3163/}
}
Tanaka, Hiromu. Minimal model program for excellent surfaces. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 345-376. doi : 10.5802/aif.3163. http://archive.numdam.org/articles/10.5802/aif.3163/

[1] Bădescu, Lucian Algebraic surfaces, Universitext, Springer, 2001, xii+258 pages (Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author) | Article | MR 1805816 | Zbl 0965.14001

[2] Beauville, Arnaud Complex algebraic surfaces, London Mathematical Society Lecture Note Series, 68, Cambridge University Press, 1983, iv+132 pages (Translated from the French by R. Barlow, N. I. Shepherd-Barron and M. Reid) | MR 732439 | Zbl 0512.14020

[3] Birkar, Caucher; Chen, Yifei; Zhang, Lei Iitaka’s C n,m conjecture for 3-folds over finite fields (2015) (https://arxiv.org/abs/1507.08760v2)

[4] Cascini, Paolo; Tanaka, Hiromu; Xu, Chenyang On base point freeness in positive characteristic, Ann. Sci. Éc. Norm. Supér., Volume 48 (2015) no. 5, pp. 1239-1272 | Article | MR 3429479 | Zbl 06543143

[5] Fantechi, Barbara; Göttsche, Lothar; Illusie, Luc; Kleiman, Steven L.; Nitsure, Nitin; Vistoli, Angelo Fundamental algebraic geometry: Grothendieck’s FGA explained, Mathematical Surveys and Monographs, 123, American Mathematical Society, 2005, x+339 pages | MR 2222646 | Zbl 1085.14001

[6] Fujino, Osamu Fundamental theorems for the log minimal model program, Publ. Res. Inst. Math. Sci., Volume 47 (2011) no. 3, pp. 727-789 | Article | MR 2832805 | Zbl 1234.14013

[7] Fujino, Osamu Minimal model theory for log surfaces, Publ. Res. Inst. Math. Sci., Volume 48 (2012) no. 2, pp. 339-371 | Article | MR 2928144 | Zbl 1248.14018

[8] Fujino, Osamu; Tanaka, Hiromu On log surfaces, Proc. Japan Acad. Ser. A, Volume 88 (2012) no. 8, pp. 109-114 | Article | MR 2989060 | Zbl 1268.14012

[9] Hacon, Christopher D.; Xu, Chenyang On finiteness of B-representations and semi-log canonical abundance, Minimal models and extremal rays (Kyoto, 2011) (Advanced Studies in Pure Mathematics), Volume 70, Mathematical Society of Japan, 2016, pp. 361-377 | MR 3618266 | Zbl 1369.14024

[10] Hartshorne, Robin Residues and duality, Lecture Notes in Mathematics, 20, Springer, 1966, vii+423 pages (with an appendix by P. Deligne) | MR 0222093 | Zbl 0212.26101

[11] Hartshorne, Robin Algebraic geometry, Graduate Texts in Mathematics, 52, Springer, 1977, xvi+496 pages | MR 0463157 | Zbl 0367.14001

[12] Kawamata, Yujiro; Matsuda, Katsumi; Matsuki, Kenji Introduction to the minimal model problem, Algebraic geometry (Sendai, 1985) (Advanced Studies in Pure Mathematics), Volume 10, North-Holland, 1987, pp. 283-360 | MR 946243 | Zbl 0672.14006

[13] Keel, Seán Basepoint freeness for nef and big line bundles in positive characteristic, Ann. Math., Volume 149 (1999) no. 1, pp. 253-286 | Article | MR 1680559 | Zbl 0954.14004

[14] Keeler, Dennis S. Ample filters of invertible sheaves, J. Algebra, Volume 259 (2003) no. 1, pp. 243-283 | Article | MR 1953719 | Zbl 1082.14004

[15] Kleiman, Steven L. Toward a numerical theory of ampleness, Ann. Math., Volume 84 (1966), pp. 293-344 | Article | MR 0206009 | Zbl 0146.17001

[16] Kollár, János Singularities of the minimal model program, Cambridge Tracts in Mathematics, 200, Cambridge University Press, 2013, x+370 pages (With a collaboration of Sándor Kovács) | Article | MR 3057950 | Zbl 1282.14028

[17] Kollár, János; Kovács, Sándor Birational geometry of log surfaces (preprint available at https://sites.math.washington.edu/~kovacs/pdf/BiratLogSurf.pdf)

[18] Kollár, János; Mori, Shigefumi Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998, viii+254 pages (With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original) | Article | MR 1658959 | Zbl 0926.14003

[19] Lazarsfeld, Robert Positivity in algebraic geometry. I: Classical setting: Line bundles and linear series, Springer, 2004, xviii+387 pages | Zbl 1066.14021

[20] Lazarsfeld, Robert Positivity in algebraic geometry. II: Positivity for vector bundles, and multiplier ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3 Folge., 49, Springer, 2004, xvii+385 pages | Article | MR 2095472 | Zbl 1093.14500

[21] Lipman, Joseph Desingularization of two-dimensional schemes, Ann. Math., Volume 107 (1978) no. 1, pp. 151-207 | Article | MR 0491722 | Zbl 0349.14004

[22] Liu, Qing Algebraic geometry and arithmetic curves, Oxford Graduate Texts in Mathematics, 6, Oxford University Press, 2002, xvi+576 pages (Translated from the French by Reinie Erné) | MR 1917232 | Zbl 1103.14001

[23] Matsumura, Hideyuki Commutative ring theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge University Press, 1989, xiv+320 pages (Translated from the Japanese by M. Reid) | MR 1011461 | Zbl 0666.13002

[24] Miyanishi, Masayoshi Noncomplete algebraic surfaces, Lecture Notes in Mathematics, 857, Springer, 1981, xviii+244 pages | MR 635930 | Zbl 0456.14018

[25] Sakai, Fumio Classification of normal surfaces, Algebraic geometry, Bowdoin 1985 (Brunswick, 1985) (Proceedings of Symposia in Pure Mathematics), Volume 46, American Mathematical Society, 1987, pp. 451-465 | MR 927967 | Zbl 0626.00011

[26] Schwede, Karl F-adjunction, Algebra Number Theory, Volume 3 (2009) no. 8, pp. 907-950 | Article | MR 2587408 | Zbl 1209.13013

[27] Schwede, Karl; Tucker, Kevin On the behavior of test ideals under finite morphisms, J. Algebr. Geom., Volume 23 (2014) no. 3, pp. 399-443 | Article | MR 3205587 | Zbl 1327.14173

[28] Seidenberg, Abraham The hyperplane sections of normal varieties, Trans. Am. Math. Soc., Volume 69 (1950), pp. 357-386 | Article | MR 0037548 | Zbl 0040.23501

[29] Shafarevich, I. R. Lectures on minimal models and birational transformations of two dimensional schemes, Tata Institute of Fundamental Research Lectures on Mathematics and Physics. Mathematics, 37, Tata Institute of Fundamental Research, 1966, iv+175 pages | MR 0217068 | Zbl 0164.51704

[30] Tanaka, Hiromu Minimal models and abundance for positive characteristic log surfaces, Nagoya Math. J., Volume 216 (2014), pp. 1-70 | Article | MR 3319838 | Zbl 1311.14020

[31] Tanaka, Hiromu The X-method for klt surfaces in positive characteristic, J. Algebr. Geom., Volume 24 (2015) no. 4, pp. 605-628 | Article | MR 3383599 | Zbl 1338.14017

[32] Tanaka, Hiromu Behavior of canonical divisors under purely inseparable base changes (2016) (https://arxiv.org/abs/1502.01381v4, to appear in J. Reine Angew. Math.)

[33] Tanaka, Hiromu Pathologies on Mori fibre spaces in positive characteristic (2016) (https://arxiv.org/abs/1609.00574v2)