|
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
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
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:
-
- [Be]
- J. N. Bernstein, Analytic continuation of generalized functions with respect to a parameter, Funk. Anal. 6 (1972), 26-40. MR 0320735 (47:9269)
- [BMS1]
- 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)
- [BMS3]
- N. Budur, M. Mustata and M. Saito, Bernstein-Sato polynomials of arbitrary varieties, Compos. Math. 142 (2006), 779-797. MR 2231202 (2007c:32036)
- [De]
- 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)
- [DH]
- J. Denef and K. Hoornaert, Newton polyhedra and Igusa's local zeta function, J. Number Theory 89 (2001), 31-64. MR 1838703 (2002g:11170)
- [DL]
- J. Denef and F. Loeser, Motivic Igusa zeta functions, J. Algebraic Geom. 7 (1998), 505-537. MR 1618144 (99j:14021)
- [Fu]
- W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, The William H. Roever Lectures in Geometry, Princeton University Press, Princeton, NJ, 1993. MR 1234037 (94g:14028)
- [Ig]
- J.-i. Igusa, An introduction to the theory of local zeta functions, AMS/IP Studies in Advanced Mathematics, 14, American Mathematical Society, Providence, RI; International Press, Cambridge, MA, 2000. MR 1743467 (2001j:11112)
- [Lo]
- F. Loeser, Fonctions d'Igusa
 -adiques, polynômes de Bernstein, et polyhédres de Newton, J. Reine Angew. Math. 412 (1990), 75-96. MR 1079002 (92c:11139) - [SS]
- M. Sato and T. Shintani, On zeta functions associated with prehomogeneous vector spaces, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1081-1082. MR 0296079 (45:5140)
- [Ve]
- W. Veys, Embedded resolution of singularities and Igusa's local zeta function, Academiae Analecta (2001), available at wis.kuleuven.be/algebra/veys.htm.
- [Zu]
- W. A. Zú
 iga-Galindo, On the poles of the Igusa zeta function for algebraic sets, Bull. London Math. Soc. 36 (2004), 310-320. MR 2038719 (2005c:11149)
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
14B05,
14M25
Retrieve articles in all Journals with MSC
(2000):
14B05,
14M25
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.
|
Comments: webmaster@ams.org