The Gauss-Manin system of an ICIS

TL;DR

This paper investigates the Gauss-Manin system of an isolated complete intersection singularity (ICIS), exploring its Hodge filtration, relation to Brieskorn lattices, and conditions for microlocal structures, linking residues to the b-function.

Contribution

It introduces a new framework connecting the Gauss-Manin system, Hodge filtration, and Brieskorn lattices for ICIS, and establishes conditions for microlocal structures.

Findings

Relation between Hodge filtration and generalized Brieskorn lattice

Conditions for the existence of microlocal structures

Connection between residues on Brieskorn lattice and b-function

Abstract

For an isolated complete intersection singularity (ICIS), we define and study its Gauss-Manin system and its associated Hodge filtration. We show the relation between the Hodge filtration and a generalized Brieskorn lattice and study conditions for the existence of a microlocal structure. Using these ideas, we relate the residue on the saturated Brieskorn lattice with a $b$-function introduced by Torrelli.