Effective finite generation for adjoint rings

Paolo Cascini[1]; De-Qi Zhang[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)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 1, page 127-144
  • ISSN: 0373-0956

Abstract

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

How to cite

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Cascini, Paolo, and Zhang, De-Qi. "Effective finite generation for adjoint rings." Annales de l’institut Fourier 64.1 (2014): 127-144. <http://eudml.org/doc/275644>.

@article{Cascini2014,
abstract = {We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.},
affiliation = {Imperial College London Department of Mathematics 180 Queen’s Gate London SW7 2AZ (United Kingdom); National University of Singapore Department of Mathematics 2 Science Drive 2 Singapore 117543 (Singapore)},
author = {Cascini, Paolo, Zhang, De-Qi},
journal = {Annales de l’institut Fourier},
keywords = {birational geometry; minimal model program; log canonical ring},
language = {eng},
number = {1},
pages = {127-144},
publisher = {Association des Annales de l’institut Fourier},
title = {Effective finite generation for adjoint rings},
url = {http://eudml.org/doc/275644},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Cascini, Paolo
AU - Zhang, De-Qi
TI - Effective finite generation for adjoint rings
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 1
SP - 127
EP - 144
AB - We describe a bound on the degree of the generators for some adjoint rings on surfaces and threefolds.
LA - eng
KW - birational geometry; minimal model program; log canonical ring
UR - http://eudml.org/doc/275644
ER -

References

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  1. F. Ambro, The moduli b -divisor of an lc-trivial fibration, Compos. Math. 141 (2005), 385-403 Zbl1094.14025MR2134273
  2. Caucher Birkar, Paolo Cascini, Christopher D. Hacon, James McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), 405-468 Zbl1210.14019MR2601039
  3. Egbert Brieskorn, Rationale Singularitäten komplexer Flächen, Invent. Math. 4 (1967/1968), 336-358 Zbl0219.14003MR222084
  4. Paolo Cascini, Vladimir Lazić, New outlook on the minimal model program, I, Duke Math. J. 161 (2012), 2415-2467 Zbl1261.14007MR2972461
  5. Jungkai A. Chen, Meng Chen, Explicit birational geometry of 3-folds of general type, II, J. Differential Geom. 86 (2010), 237-271 Zbl1218.14026MR2772551
  6. Jungkai A. Chen, Meng Chen, Explicit birational geometry of threefolds of general type, I, Ann. Sci. Éc. Norm. Supér. (4) 43 (2010), 365-394 Zbl1194.14060MR2667020
  7. Jungkai A. Chen, Christopher D. Hacon, Factoring 3-fold flips and divisorial contractions to curves, J. Reine Angew. Math. 657 (2011), 173-197 Zbl1230.14015MR2824787
  8. A. Corti, V. Lazić, New outlook on Mori theory, II, (2010) Zbl1273.14033
  9. M.L. Green, The canonical ring of a variety of general type, Duke Math. J. 49 (1982), 1087-1113 Zbl0607.14005MR683012
  10. Christopher D. Hacon, James McKernan, Boundedness of pluricanonical maps of varieties of general type, Invent. Math. 166 (2006), 1-25 Zbl1121.14011MR2242631
  11. T. Hayakawa, Blowing ups of 3 -dimensional terminal singularities, Publ. Res. Inst. Math. Sci. 35 (1999), 515-570 Zbl0969.14008MR1710753
  12. T. Hayakawa, Blowing ups of 3-dimensional terminal singularities. II, Publ. Res. Inst. Math. Sci. 36 (2000), 423-456 Zbl1017.14006MR1781436
  13. Yujiro Kawamata, The minimal discrepancy of a 3 -fold terminal singularity, (1993) Zbl0857.14010
  14. Yujiro Kawamata, Subadjunction of log canonical divisors. II, Amer. J. Math. 120 (1998), 893-899 Zbl0919.14003MR1646046
  15. János Kollár, Effective base point freeness, Math. Ann. 296 (1993), 595-605 Zbl0818.14002MR1233485
  16. János Kollár, Shigefumi Mori, Birational geometry of algebraic varieties, 134 (1998), Cambridge University Press, Cambridge Zbl0926.14003
  17. R. Lazarsfeld, Positivity in Algebraic Geometry. I, 48 (2004), Springer-Verlag, Berlin Zbl1093.14500MR2095471
  18. Shigefumi Mori, On 3 -dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66 Zbl0589.14005MR792770
  19. Y. Prokhorov, V. Shokurov, Towards the second main theorem on complements, J. Algebraic Geom. 18 (2009), 151-199 Zbl1159.14020MR2448282
  20. Miles Reid, Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985) 46 (1987), 345-414, Amer. Math. Soc., Providence, RI Zbl0634.14003MR927963
  21. Y.-T. Siu, Finite generation of canonical ring by analytic method, Sci. China Ser. A 51 (2008), 481-502 Zbl1153.32021MR2395400
  22. Shigeharu Takayama, Pluricanonical systems on algebraic varieties of general type, Invent. Math. 165 (2006), 551-587 Zbl1108.14031MR2242627
  23. G. Todorov, C. Xu, On Effective log Iitaka fibration for 3-folds and 4-folds, Algebra Number Theory 3 (2009), 697-710 Zbl1184.14023MR2579391
  24. E. Viehweg, D.-Q. Zhang, Effective Iitaka fibrations, J. Algebraic Geom. 18 (2009), 711-730 Zbl1177.14039MR2524596

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