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 .
Accepted:
DOI: 10.5802/aif.2841
Classification: 14E30, 14E99
Keywords: birational geometry, minimal model program, log canonical ring
@article{AIF_2014__64_1_127_0, author = {Cascini, Paolo and Zhang, De-Qi}, title = {Effective finite generation for adjoint rings}, journal = {Annales de l'Institut Fourier}, pages = {127--144}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {1}, year = {2014}, doi = {10.5802/aif.2841}, zbl = {06387268}, mrnumber = {3330543}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2841/} }
TY - JOUR TI - Effective finite generation for adjoint rings JO - Annales de l'Institut Fourier PY - 2014 DA - 2014/// SP - 127 EP - 144 VL - 64 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2841/ UR - https://zbmath.org/?q=an%3A06387268 UR - https://www.ams.org/mathscinet-getitem?mr=3330543 UR - https://doi.org/10.5802/aif.2841 DO - 10.5802/aif.2841 LA - en ID - AIF_2014__64_1_127_0 ER -
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] The moduli -divisor of an lc-trivial fibration, Compos. Math., Tome 141 (2005) no. 2, pp. 385-403 | Article | MR: 2134273 | Zbl: 1094.14025
[2] Existence of minimal models for varieties of log general type, J. Amer. Math. Soc., Tome 23 (2010) no. 2, pp. 405-468 | Article | MR: 2601039 | Zbl: 1210.14019
[3] Rationale Singularitäten komplexer Flächen, Invent. Math., Tome 4 (1967/1968), pp. 336-358 | Article | MR: 222084 | Zbl: 0219.14003
[4] New outlook on the minimal model program, I, Duke Math. J., Tome 161 (2012) no. 12, pp. 2415-2467 | Article | MR: 2972461 | Zbl: 1261.14007
[5] Explicit birational geometry of 3-folds of general type, II, J. Differential Geom., Tome 86 (2010) no. 2, pp. 237-271 http://projecteuclid.org/getRecord?id=euclid.jdg/1299766788 | MR: 2772551 | Zbl: 1218.14026
[6] Explicit birational geometry of threefolds of general type, I, Ann. Sci. Éc. Norm. Supér. (4), Tome 43 (2010) no. 3, pp. 365-394 | Numdam | MR: 2667020 | Zbl: 1194.14060
[7] Factoring 3-fold flips and divisorial contractions to curves, J. Reine Angew. Math., Tome 657 (2011), pp. 173-197 | Article | MR: 2824787 | Zbl: 1230.14015
[8] New outlook on Mori theory, II, 2010 (arXiv:1005.0614v2)
[9] The canonical ring of a variety of general type, Duke Math. J., Tome 49 (1982) no. 4, pp. 1087-1113 http://projecteuclid.org/getRecord?id=euclid.dmj/1077315540 | Article | MR: 683012 | Zbl: 0607.14005
[10] Boundedness of pluricanonical maps of varieties of general type, Invent. Math., Tome 166 (2006) no. 1, pp. 1-25 | Article | MR: 2242631 | Zbl: 1121.14011
[11] Blowing ups of -dimensional terminal singularities, Publ. Res. Inst. Math. Sci., Tome 35 (1999) no. 3, pp. 515-570 | Article | MR: 1710753 | Zbl: 0969.14008
[12] Blowing ups of 3-dimensional terminal singularities. II, Publ. Res. Inst. Math. Sci., Tome 36 (2000) no. 3, pp. 423-456 | Article | MR: 1781436 | Zbl: 1017.14006
[13] The minimal discrepancy of a -fold terminal singularity, 1993 (Appendix to [21])
[14] Subadjunction of log canonical divisors. II, Amer. J. Math., Tome 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] Effective base point freeness, Math. Ann., Tome 296 (1993) no. 4, pp. 595-605 | Article | MR: 1233485 | Zbl: 0818.14002
[16] Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, Tome 134, Cambridge University Press, Cambridge, 1998, viii+254 pages (With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original) | Article | Zbl: 0926.14003
[17] Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Tome 48, Springer-Verlag, Berlin, 2004 | MR: 2095471 | Zbl: 1093.14500
[18] On -dimensional terminal singularities, Nagoya Math. J., Tome 98 (1985), pp. 43-66 http://projecteuclid.org/getRecord?id=euclid.nmj/1118787793 | MR: 792770 | Zbl: 0589.14005
[19] Towards the second main theorem on complements, J. Algebraic Geom., Tome 18 (2009) no. 1, pp. 151-199 | Article | MR: 2448282 | Zbl: 1159.14020
[20] Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) (Proc. Sympos. Pure Math.) Tome 46, Amer. Math. Soc., Providence, RI, 1987, pp. 345-414 | MR: 927963 | Zbl: 0634.14003
[21] Finite generation of canonical ring by analytic method, Sci. China Ser. A, Tome 51 (2008) no. 4, pp. 481-502 | Article | MR: 2395400 | Zbl: 1153.32021
[22] Pluricanonical systems on algebraic varieties of general type, Invent. Math., Tome 165 (2006) no. 3, pp. 551-587 | Article | MR: 2242627 | Zbl: 1108.14031
[23] On Effective log Iitaka fibration for 3-folds and 4-folds, Algebra Number Theory, Tome 3 (2009) no. 6, pp. 697-710 | Article | MR: 2579391 | Zbl: 1184.14023
[24] Effective Iitaka fibrations, J. Algebraic Geom., Tome 18 (2009) no. 4, pp. 711-730 | Article | MR: 2524596 | Zbl: 1177.14039
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