Available in electronic format
Available in print format
Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
     

Multiplier ideals of monomial ideals

Author(s): J. A. Howald
Journal: Trans. Amer. Math. Soc. 353 (2001), 2665-2671.
MSC (2000): Primary 14Q99; Secondary 14M25
Posted: March 2, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract:

In this note we discuss a simple algebraic calculation of the multiplier ideal associated to a monomial ideal in affine $n$-space. We indicate how this result allows one to compute not only the multiplier ideal but also the log canonical threshold of an ideal in terms of its Newton polygon.


References:

1.
Urban Angehrn and Yum Tong Siu. Effective freeness and point separation for adjoint bundles. Invent. Math., 122(2):291-308, 1995. MR 97b:32036

2.
V. I. Arnol'd, S. M. Gusein-Zade, and A. N. Varchenko. Singularities of Differentiable Maps. Vol. I. Birkhäuser Boston Inc., Boston, Mass., 1985. MR 86f:58018

3.
Jean-Pierre Demailly. $L^2$ vanishing theorems for positive line bundles and adjunction theory. In Transcendental methods in algebraic geometry (Cetraro, 1994), Lecture Notes in Math., vol. 1646, pages 1-97. Springer, Berlin, 1996. MR 99k:32051

4.
Jean-Pierre Demailly and János Kollár. Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Mathematics E-Print Archive, October 1999.

5.
Lawrence Ein. Multiplier ideals, vanishing theorems and applications. In Algebraic geometry--Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, part 1, pages 203-219. Amer. Math. Soc., Providence, RI, 1997. MR 98m:14006

6.
Lawrence Ein and Robert Lazarsfeld. A geometric effective Nullstellensatz. Invent. Math., 137(2):427-448, 1999. MR 2000j:14028

7.
David Eisenbud. Commutative Algebra. With a View toward Algebraic Geometry. Springer-Verlag, New York, 1995. MR 87a:13001

8.
William Fulton. Introduction to Toric Varieties. Princeton University Press, Princeton, NJ, 1993. MR 94g:14028

9.
János Kollár. Singularities of pairs. In Algebraic geometry--Santa Cruz 1995, pages 221-287. Proc. Sympos. Pure Math., vol. 62, part 1, Amer. Math. Soc., Providence, RI, 1997. MR 99m:14033

10.
Maclagan. Antichains of monomial ideals are finite. Mathematics E-Print Archive, October 1999.

11.
V. V. Shokurov. $3$-fold log flips. Izv. Ross. Akad. Nauk Ser. Mat., 56:105-203, 1992; English transl., Russian Acad. Sci. Izv. Math. 40:95-202, 1993. MR 93j:14012

12.
Yum-Tong Siu. Invariance of plurigenera. Invent. Math., 134(3):661-673, 1998. MR 99i:32035


Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14Q99, 14M25

Retrieve articles in all Journals with MSC (2000): 14Q99, 14M25


Additional Information:

J. A. Howald
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48104
Email: jahowald@math.lsa.umich.edu

DOI: 10.1090/S0002-9947-01-02720-9
PII: S 0002-9947(01)02720-9
Received by editor(s): April 10, 2000
Posted: March 2, 2001
Additional Notes: I would like to thank Robert Lazarsfeld for suggesting this problem, and for many valuable discussions.
Copyright of article: Copyright 2001, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google