On D-modules related to the b-function and Hamiltonian flow
File(s)
Accepted version
Author(s)
Bitoun, Thomas
Schedler, TJ
Type
Journal Article
Abstract
Let f be a quasi-homogeneous polynomial with an isolated singularity in Cn . We compute the length of the D -modules Df𝜆/Df𝜆+1 generated by complex powers of f in terms of the Hodge filtration on the top cohomology of the Milnor fiber. When 𝜆=−1 we obtain one more than the reduced genus of the singularity ( dimHn−2(Z,OZ) for Z the exceptional fiber of a resolution of singularities). We conjecture that this holds without the quasi-homogeneous assumption. We also deduce that the quotient Df𝜆/Df𝜆+1 is nonzero when 𝜆 is a root of the b -function of f (which Saito recently showed fails to hold in the inhomogeneous case). We obtain these results by comparing these D -modules to those defined by Etingof and the second author which represent invariants under Hamiltonian flow.
Date Issued
2018-11-01
Date Acceptance
2018-04-03
Citation
Compositio Mathematica, 2018, 154 (11), pp.2426-2440
ISSN
0010-437X
Publisher
Cambridge University Press
Start Page
2426
End Page
2440
Journal / Book Title
Compositio Mathematica
Volume
154
Issue
11
Sponsor
National Science Foundation
Identifier
https://www.cambridge.org/core/journals/compositio-mathematica/article/on-mathcald-modules-related-to-the-b-function-and-hamiltonian-flow/7AA8B9B35FBBA71CAB38FBBBF15ED225
Grant Number
DMS-1406553
Subjects
0101 Pure Mathematics
General Mathematics
Publication Status
Published
Date Publish Online
2018-10-12