Title: Zeta functions and Bernstein-Sato polynomials for ideals in dimension two
Authors: Bories, Bart # ×
Issue Date: 2013
Publisher: Springer Italia Srl
Series Title: Revista Matematica Complutense vol:26 issue:2 pages:753-772
Article number: MR3068618
Abstract: For a nonzero ideal I of C[x_1,...,x_n], with 0 in supp I, a generalization of a conjecture of Igusa - Denef - Loeser predicts that every pole of its topological zeta function is a root of its Bernstein-Sato polynomial. However, typically only a few roots are obtained this way. Following ideas of Veys, we study the following question. Is it possible to find a collection G of polynomials g in C[x_1,...,x_n], such that, for all g in G, every pole of the topological zeta function associated to I and the volume form gdx on the affine n-space, is a root of the Bernstein-Sato polynomial of I, and such that all roots are realized in this way. We obtain a negative answer to this question, providing counterexamples for monomial and principal ideals in dimension two, and give a partial positive result as well.
ISSN: 1139-1138
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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