Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Multiplier ideals of monomial ideals

Author: J. A. Howald
Journal: Trans. Amer. Math. Soc. 353 (2001), 2665-2671
MSC (2000): Primary 14Q99; Secondary 14M25
Published electronically: March 2, 2001
MathSciNet review: 1828466
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


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

  • 1. Urban Angehrn and Yum Tong Siu, Effective freeness and point separation for adjoint bundles, Invent. Math. 122 (1995), no. 2, 291–308. MR 1358978, 10.1007/BF01231446
  • 2. V. I. Arnol′d, S. M. Guseĭn-Zade, and A. N. Varchenko, Singularities of differentiable maps. Vol. I, Monographs in Mathematics, vol. 82, Birkhäuser Boston, Inc., Boston, MA, 1985. The classification of critical points, caustics and wave fronts; Translated from the Russian by Ian Porteous and Mark Reynolds. MR 777682
  • 3. Jean-Pierre Demailly, 𝐿² vanishing theorems for positive line bundles and adjunction theory, Transcendental methods in algebraic geometry (Cetraro, 1994) Lecture Notes in Math., vol. 1646, Springer, Berlin, 1996, pp. 1–97. MR 1603616, 10.1007/BFb0094302
  • 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, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 203–219. MR 1492524
  • 6. Lawrence Ein and Robert Lazarsfeld, A geometric effective Nullstellensatz, Invent. Math. 137 (1999), no. 2, 427–448. MR 1705839, 10.1007/s002220050332
  • 7. Topics related to cohomologies of local rings, Kyoto University, Research Institute for Mathematical Sciences, Kyoto, 1985 (Japanese). Sūrikaisekikenkyūsho Kōkyūroku No. 543 (1985). MR 836166
  • 8. William Fulton, Introduction to toric varieties, Annals of Mathematics Studies, vol. 131, Princeton University Press, Princeton, NJ, 1993. The William H. Roever Lectures in Geometry. MR 1234037
  • 9. János Kollár, Singularities of pairs, Algebraic geometry—Santa Cruz 1995, Proc. Sympos. Pure Math., vol. 62, Amer. Math. Soc., Providence, RI, 1997, pp. 221–287. MR 1492525
  • 10. Maclagan. Antichains of monomial ideals are finite. Mathematics E-Print Archive, October 1999.
  • 11. V. V. Shokurov, Three-dimensional log perestroikas, Izv. Ross. Akad. Nauk Ser. Mat. 56 (1992), no. 1, 105–203 (Russian); English transl., Russian Acad. Sci. Izv. Math. 40 (1993), no. 1, 95–202. MR 1162635, 10.1070/IM1993v040n01ABEH001862
  • 12. Yum-Tong Siu, Invariance of plurigenera, Invent. Math. 134 (1998), no. 3, 661–673. MR 1660941, 10.1007/s002220050276

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

Received by editor(s): April 10, 2000
Published electronically: March 2, 2001
Additional Notes: I would like to thank Robert Lazarsfeld for suggesting this problem, and for many valuable discussions.
Article copyright: © Copyright 2001 American Mathematical Society