Nous établissons une borne sur le degré des générateurs pour les anneaux adjoints de surfaces et de variétés algébriques de dimension .
We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.
@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}, volume = {64}, year = {2014}, pages = {127-144}, doi = {10.5802/aif.2841}, zbl = {06387268}, mrnumber = {3330543}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_2014__64_1_127_0} }
Cascini, Paolo; Zhang, De-Qi. Effective finite generation for adjoint rings. Annales de l'Institut Fourier, Tome 64 (2014) pp. 127-144. doi : 10.5802/aif.2841. http://gdmltest.u-ga.fr/item/AIF_2014__64_1_127_0/
[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 University Press, Cambridge, Cambridge Tracts in Mathematics, Tome 134 (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] Positivity in Algebraic Geometry. I, Springer-Verlag, Berlin, Ergebnisse der Mathematik und ihrer Grenzgebiete, Tome 48 (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), Amer. Math. Soc., Providence, RI (Proc. Sympos. Pure Math.) Tome 46 (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