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On Igusa zeta functions of monomial ideals
Author(s):
Jason
Howald;
Mircea
Mustata;
Cornelia
Yuen
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3425-3433.
MSC (2000):
Primary 14B05;
Secondary 14M25
Posted:
August 6, 2007
MathSciNet review:
2336554
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Abstract:
We show that the real parts of the poles of the Igusa zeta function of a monomial ideal can be computed from the torus-invariant divisors on the normalized blow-up of the affine space along the ideal. Moreover, we show that every such number is a root of the Bernstein-Sato polynomial associated to the monomial ideal.
References:
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- N. Budur, M. Mustata and M. Saito, Combinatorial description of the roots of the Bernstein-Sato polynomials for monomial ideals, Comm. Algebra. 34 (2006), 4103-4117. MR 2267574 (2007h:32041)
- [BMS2]
- N. Budur, M. Mustata and M. Saito, Roots of Bernstein-Sato polynomials for monomial ideals: a positive characteristic approach, Math. Res. Lett. 13 (2006), 125-142. MR 2200051 (2006k:14003)
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- N. Budur, M. Mustata and M. Saito, Bernstein-Sato polynomials of arbitrary varieties, Compos. Math. 142 (2006), 779-797. MR 2231202 (2007c:32036)
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- J. Denef, Report on Igusa's local zeta function, Séminaire Bourbaki, Vol. 1990/91, Astérisque No. 201-203 (1991), Exp. No. 741, 359-386. MR 1157848 (93g:11119)
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Additional Information:
Jason
Howald
Affiliation:
Department of Mathematics and Computer Science, John Carroll University, 20700 North Park Blvd., University Heights, Ohio 44118
Address at time of publication:
Department of Mathematics, SUNY Potsdam, 44 Pierrepont Avenue, Potsdam, New York 13676-2294
Email:
howaldja@potsdam.edu
Mircea
Mustata
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email:
mmustata@umich.edu
Cornelia
Yuen
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Address at time of publication:
Department of Mathematics, University of Kentucky, 825 Patterson Office Tower, Lexington, Kentucky 40506
Email:
cyuen@ms.uky.edu
DOI:
10.1090/S0002-9939-07-08957-5
PII:
S 0002-9939(07)08957-5
Keywords:
Igusa zeta function,
monomial ideal,
Bernstein-Sato polynomial
Received by editor(s):
June 15, 2006
Posted:
August 6, 2007
Additional Notes:
The research of the second author was partially supported by NSF grant DMS 0500127
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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