Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

A subadditivity formula for multiplier ideals associated to log pairs


Author: Shunsuke Takagi
Journal: Proc. Amer. Math. Soc. 141 (2013), 93-102
MSC (2010): Primary 14F18; Secondary 13A35, 14B05, 14E15
Published electronically: May 11, 2012
MathSciNet review: 2988713
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: As a generalization of formulas given in earlier papers by Demailly-Ein-Lazarsfeld, Eisenstein and Takagi, we prove a subadditivity formula for multiplier ideals associated to log pairs.


References [Enhancements On Off] (What's this?)

  • 1. M. Blickle, K. Schwede, S. Takagi and W. Zhang, Discreteness and rationality of $ F$-jumping numbers on singular varieties, Math. Ann. 347 (2010), 917-949. MR 2658149
  • 2. S. Boucksom, T. de Fernex and C. Favre, The volume of an isolated singularity, http://arxiv.
    org/abs/1011.2847, to appear in Duke Math. J.
  • 3. A. Bravo, S. Encinas and O. Villamayor, A simplified proof of desingularization and applications, Rev. Mat. Iberoamericana 21 (2005), 349-458. MR 2174912 (2006h:14018)
  • 4. J.-P. Demailly, L. Ein and R. Lazarsfeld, A subadditivity property of multiplier ideals, Michigan Math. J. 48 (2000), 137-156. MR 1786484 (2002a:14016)
  • 5. L. Ein, R. Lazarsfeld, and K. Smith, Uniform bounds and symbolic powers on smooth varieties, Invent. Math. 144 (2001), 241-252. MR 1826369 (2002b:13001)
  • 6. L. Ein, R. Lazarsfeld, and K. Smith, Uniform approximation of Abhyankar valuation ideals in smooth function fields, Amer. J. Math. 125 (2003), 409-440. MR 1963690 (2003m:13004)
  • 7. E. Eisenstein, Generalization of the restriction theorem for multiplier ideals, arXiv:1001.2841, to appear in Ann. Inst. Fourier (Grenoble).
  • 8. T. Fujita, Approximating Zariski decomposition of big line bundles, Kodai Math. J. 17 (1994), 1-3. MR 1262949 (95c:14053)
  • 9. N. Hara and S. Takagi, On a generalization of test ideals, Nagoya Math. J. 175 (2004), 59-74. MR 2085311 (2005g:13009)
  • 10. N. Hara and K. Yoshida, A generalization of tight closure and multiplier ideals, Trans. Amer. Math. Soc. 355 (2003), 3143-3174. MR 1974679 (2004i:13003)
  • 11. M. Hochster and C. Huneke, Tight closure in equal characteristic zero, preprint.
  • 12. M. Kawakita, On a comparison of minimal log discrepancies in terms of motivic integration, J. Reine Angew. Math. 620 (2008), 55-65. MR 2427975 (2010i:14021)
  • 13. R. Lazarsfeld, Positivity in Algebraic Geometry II, Ergeb. Math. Grenzgeb. 3. Folge, A Series of Modern Surveys in Mathematics, vol. 49, Springer-Verlag, Berlin, 2004. MR 2095472 (2005k:14001b)
  • 14. M. McDermott, Test ideals in diagonal hypersurface rings. II, J. Algebra 264 (2003), 296-304. MR 1980699 (2004d:13004)
  • 15. M. Mustaţa and V. Srinivas, Ordinary varieties and the comparison between multiplier ideals and test ideals, Nagoya Math. J. 204 (2011), 125-157. MR 2863367
  • 16. K. Schwede, Centers of $ F$-purity, Math. Z. 265 (2010), 687-714. MR 2644316 (2011e:13011)
  • 17. S. Takagi, An interpretation of multiplier ideals via tight closure, J. Algebraic Geom. 13 (2004), 393-415. MR 2047704 (2005c:13002)
  • 18. S. Takagi, Formulas for multiplier ideals on singular varieties, Amer. J. Math. 128 (2006), no. 6, 1345-1362. MR 2275023 (2007i:14006)
  • 19. S. Takagi and K. Yoshida, Generalized test ideals and symbolic powers, Michigan Math. J. 57 (2008), 711-724. MR 2492477 (2010d:13007)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14F18, 13A35, 14B05, 14E15

Retrieve articles in all journals with MSC (2010): 14F18, 13A35, 14B05, 14E15


Additional Information

Shunsuke Takagi
Affiliation: Department of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan
Address at time of publication: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Email: stakagi@math.kyushu-u.ac.jp, stakagi@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11368-1
Received by editor(s): June 9, 2011
Published electronically: May 11, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.