Effective finite generation for adjoint rings
Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 127-144.

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

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

DOI: 10.5802/aif.2841
Classification: 14E30, 14E99
Keywords: birational geometry, minimal model program, log canonical ring
Mot clés : géométrie birationnelle, programme du modèle minimal, anneau log-canonique

Cascini, Paolo 1; Zhang, De-Qi 2

1 Imperial College London Department of Mathematics 180 Queen’s Gate London SW7 2AZ (United Kingdom)
2 National University of Singapore Department of Mathematics 2 Science Drive 2 Singapore 117543 (Singapore)
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Cascini, Paolo; Zhang, De-Qi. Effective finite generation for adjoint rings. Annales de l'Institut Fourier, Volume 64 (2014) no. 1, pp. 127-144. doi : 10.5802/aif.2841. https://aif.centre-mersenne.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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

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

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

[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 | Zbl

[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 | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

[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 | DOI | MR | Zbl

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

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

[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 | DOI | MR | Zbl

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

[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) | DOI | Zbl

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

[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 | Zbl

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

[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 | Zbl

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

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

[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 | DOI | MR | Zbl

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

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