no. 1
Effective finite generation for adjoint rings
[Génération finie effective d’anneaux adjoints]
Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 127-144.

Nous établissons une borne sur le degré des générateurs pour les anneaux adjoints de surfaces et de variétés algébriques de dimension 3.

We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.

DOI : https://doi.org/10.5802/aif.2841
Classification : 14E30,  14E99
Mots clés : géométrie birationnelle, programme du modèle minimal, anneau log-canonique 
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Cascini, Paolo; Zhang, De-Qi. Effective finite generation for adjoint rings. Annales de l'Institut Fourier, Tome 64 (2014) no. 1, pp. 127-144. doi : 10.5802/aif.2841. http://www.numdam.org/articles/10.5802/aif.2841/

[1] Ambro, F. The moduli b-divisor of an lc-trivial fibration, Compos. Math., Volume 141 (2005) no. 2, pp. 385-403 | Article | MR 2134273 | Zbl 1094.14025

[2] Birkar, Caucher; Cascini, Paolo; Hacon, Christopher D.; McKernan, James Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., Volume 23 (2010) no. 2, pp. 405-468 | Article | MR 2601039 | Zbl 1210.14019

[3] Brieskorn, Egbert Rationale Singularitäten komplexer Flächen, Invent. Math., Volume 4 (1967/1968), pp. 336-358 | Article | MR 222084 | Zbl 0219.14003

[4] Cascini, Paolo; Lazić, Vladimir New outlook on the minimal model program, I, Duke Math. J., Volume 161 (2012) no. 12, pp. 2415-2467 | Article | MR 2972461 | Zbl 1261.14007

[5] Chen, Jungkai A.; Chen, Meng Explicit birational geometry of 3-folds of general type, II, J. Differential Geom., Volume 86 (2010) no. 2, pp. 237-271 http://projecteuclid.org/getRecord?id=euclid.jdg/1299766788 | MR 2772551 | Zbl 1218.14026

[6] Chen, Jungkai A.; Chen, Meng Explicit birational geometry of threefolds of general type, I, Ann. Sci. Éc. Norm. Supér. (4), Volume 43 (2010) no. 3, pp. 365-394 | Numdam | MR 2667020 | Zbl 1194.14060

[7] Chen, Jungkai A.; Hacon, Christopher D. Factoring 3-fold flips and divisorial contractions to curves, J. Reine Angew. Math., Volume 657 (2011), pp. 173-197 | Article | MR 2824787 | Zbl 1230.14015

[8] Corti, A.; Lazić, V. New outlook on Mori theory, II, 2010 (arXiv:1005.0614v2)

[9] Green, M.L. The canonical ring of a variety of general type, Duke Math. J., Volume 49 (1982) no. 4, pp. 1087-1113 http://projecteuclid.org/getRecord?id=euclid.dmj/1077315540 | Article | MR 683012 | Zbl 0607.14005

[10] Hacon, Christopher D.; McKernan, James Boundedness of pluricanonical maps of varieties of general type, Invent. Math., Volume 166 (2006) no. 1, pp. 1-25 | Article | MR 2242631 | Zbl 1121.14011

[11] Hayakawa, T. Blowing ups of 3-dimensional terminal singularities, Publ. Res. Inst. Math. Sci., Volume 35 (1999) no. 3, pp. 515-570 | Article | MR 1710753 | Zbl 0969.14008

[12] Hayakawa, T. Blowing ups of 3-dimensional terminal singularities. II, Publ. Res. Inst. Math. Sci., Volume 36 (2000) no. 3, pp. 423-456 | Article | MR 1781436 | Zbl 1017.14006

[13] Kawamata, Yujiro The minimal discrepancy of a 3-fold terminal singularity, 1993 (Appendix to [21])

[14] Kawamata, Yujiro Subadjunction of log canonical divisors. II, Amer. J. Math., Volume 120 (1998) no. 5, pp. 893-899 http://muse.jhu.edu/journals/american_journal_of_mathematics/v120/120.5kawamata.pdf | Article | MR 1646046 | Zbl 0919.14003

[15] Kollár, János Effective base point freeness, Math. Ann., Volume 296 (1993) no. 4, pp. 595-605 | Article | MR 1233485 | Zbl 0818.14002

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

[17] Lazarsfeld, R. Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, 48, Springer-Verlag, Berlin, 2004 | MR 2095471 | Zbl 1093.14500

[18] Mori, Shigefumi On 3-dimensional terminal singularities, Nagoya Math. J., Volume 98 (1985), pp. 43-66 http://projecteuclid.org/getRecord?id=euclid.nmj/1118787793 | MR 792770 | Zbl 0589.14005

[19] Prokhorov, Y.; Shokurov, V. Towards the second main theorem on complements, J. Algebraic Geom., Volume 18 (2009) no. 1, pp. 151-199 | Article | MR 2448282 | Zbl 1159.14020

[20] Reid, Miles Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) (Proc. Sympos. Pure Math.), Volume 46, Amer. Math. Soc., Providence, RI, 1987, pp. 345-414 | MR 927963 | Zbl 0634.14003

[21] Siu, Y.-T. Finite generation of canonical ring by analytic method, Sci. China Ser. A, Volume 51 (2008) no. 4, pp. 481-502 | Article | MR 2395400 | Zbl 1153.32021

[22] Takayama, Shigeharu Pluricanonical systems on algebraic varieties of general type, Invent. Math., Volume 165 (2006) no. 3, pp. 551-587 | Article | MR 2242627 | Zbl 1108.14031

[23] Todorov, G.; Xu, C. On Effective log Iitaka fibration for 3-folds and 4-folds, Algebra Number Theory, Volume 3 (2009) no. 6, pp. 697-710 | Article | MR 2579391 | Zbl 1184.14023

[24] Viehweg, E.; Zhang, D.-Q. Effective Iitaka fibrations, J. Algebraic Geom., Volume 18 (2009) no. 4, pp. 711-730 | Article | MR 2524596 | Zbl 1177.14039

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