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.

Received:
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  - 
%0 Journal Article
%T Effective finite generation for adjoint rings
%J Annales de l'Institut Fourier
%D 2014
%P 127-144
%V 64
%N 1
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.2841
%R 10.5802/aif.2841
%G en
%F AIF_2014__64_1_127_0
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., Tome 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., Tome 23 (2010) no. 2, pp. 405-468 | Article | MR: 2601039 | Zbl: 1210.14019

[3] Brieskorn, Egbert Rationale Singularitäten komplexer Flächen, Invent. Math., Tome 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., Tome 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., Tome 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), Tome 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., Tome 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., Tome 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., Tome 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., Tome 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., Tome 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., 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] Kollár, János Effective base point freeness, Math. Ann., Tome 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, 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] Lazarsfeld, R. Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Tome 48, Springer-Verlag, Berlin, 2004 | MR: 2095471 | Zbl: 1093.14500

[18] Mori, Shigefumi On 3-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] Prokhorov, Y.; Shokurov, V. 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] Reid, Miles 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] Siu, Y.-T. 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] Takayama, Shigeharu 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] Todorov, G.; Xu, C. 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] Viehweg, E.; Zhang, D.-Q. Effective Iitaka fibrations, J. Algebraic Geom., Tome 18 (2009) no. 4, pp. 711-730 | Article | MR: 2524596 | Zbl: 1177.14039

Cited by Sources: