Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multiplier ideals and integral closure of monomial ideals: An analytic approach

Authors: Jeffery D. McNeal and Yunus E. Zeytuncu
Journal: Proc. Amer. Math. Soc. 140 (2012), 1483-1493
MSC (2010): Primary 13P99, 14Q99, 32S45; Secondary 14M25, 13B22
Published electronically: August 22, 2011
MathSciNet review: 2869133
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Proofs of two results about a monomial ideal - describing membership in auxiliary ideals associated to the monomial ideal - are given which do not invoke resolution of singularities. The AM-GM inequality is used as a substitute for taking a log resolution of the monomial ideal.

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

  • 1. Manuel Blickle and Robert Lazarsfeld.
    An informal introduction to multiplier ideals.
    In Trends in commutative algebra, volume 51 of Math. Sci. Res. Inst. Publ., pages 87-114. Cambridge Univ. Press, Cambridge, 2004. MR 2132649 (2007h:14003)
  • 2. Jean-Pierre Demailly.
    Multiplier ideal sheaves and analytic methods in algebraic geometry.
    ICTP Lect. Notes (Trieste, 2000), 6:1-148, 2001. MR 1919457 (2003f:32020)
  • 3. Jean-Pierre Demailly.
    Analytic approach to the minimal model program and the abundance conjectures.
    PCMI Lect. Notes, 2008.
  • 4. Jean-Pierre Demailly, Lawrence Ein, and Robert Lazarsfeld.
    A subadditivity property of multiplier ideals.
    Michigan Math. J., 48:137-156, 2000.
    Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786484 (2002a:14016)
  • 5. Jean-Pierre Demailly and János Kollár.
    Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds.
    Ann. Sci. École Norm. Sup. (4), 34(4):525-556, 2001. MR 1852009 (2002e:32032)
  • 6. David Eisenbud.
    Commutative Algebra, with a View toward Algebraic Geometry.
    Vol. 150 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. MR 1322960 (97a:13001)
  • 7. Heisuke Hironaka.
    Resolution of singularities of an algebraic variety over a field of characteristic zero, I, II.
    Ann. of Math. (2), 79:109-203, 205-326, 1964. MR 0199184 (33:7333)
  • 8. J. A. Howald.
    Multiplier ideals of monomial ideals.
    Trans. Amer. Math. Soc., 353(7):2665-2671 (electronic), 2001. MR 1828466 (2002b:14061)
  • 9. Robert Lazarsfeld.
    Positivity in algebraic geometry. II, volume 49 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics].
    Positivity for vector bundles, and multiplier ideals.
    Springer-Verlag, Berlin, 2004. MR 2095472 (2005k:14001b)
  • 10. Monique Lejeune-Jalabert and Bernard Teissier.
    Clôture intégrale des idéaux et équisingularité.
    Ann. Fac. Sci. Toulouse Math. (6), 17(4):781-859, 2008.
    With an appendix by Jean-Jacques Risler. MR 2499856 (2010i:32026)
  • 11. Mircea Mustaţa.
    The multiplier ideals of a sum of ideals.
    Trans. Amer. Math. Soc., 354(1):205-217 (electronic), 2002. MR 1859032 (2002k:14006)
  • 12. Alan Nadel.
    Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature.
    Ann. of Math. (2), 132:549-596, 1990. MR 1078269 (92d:32038)
  • 13. Yum-Tong Siu.
    An effective Matsusaka big theorem.
    Ann. Instit. Fourier (Grenoble), 43(5):1387-1405, 1993. MR 1275204 (95f:32035)
  • 14. Yum-Tong Siu.
    Effective very ampleness.
    Invent. Math., 124(1-3):563-571, 1996. MR 1369428 (97a:32036)
  • 15. Yum-Tong Siu.
    Invariance of plurigenera.
    Invent. Math., 134(3):661-673, 1998. MR 1660941 (99i:32035)
  • 16. Yum-Tong Siu.
    Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type.
    Complex Geometry (Göttingen, 2000), Springer, Berlin, 2002, pages 223-277. MR 1922108 (2003j:32027a)
  • 17. Bernard Teissier.
    Variétés polaires. II. Multiplicités polaires, sections planes, et conditions de Whitney.
    Algebraic Geometry (La Rábida 1981), Lect. Notes in Math., 961:314-491, 1983. MR 708342 (85i:32019)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13P99, 14Q99, 32S45, 14M25, 13B22

Retrieve articles in all journals with MSC (2010): 13P99, 14Q99, 32S45, 14M25, 13B22

Additional Information

Jeffery D. McNeal
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Yunus E. Zeytuncu
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

Received by editor(s): October 22, 2009
Received by editor(s) in revised form: January 11, 2011
Published electronically: August 22, 2011
Additional Notes: Research of both authors was partially supported by NSF grants
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society