The Gauss-Manin system of an ICIS

2025/06/25 by Guillem Blanco, Blanco, Guillem
Computer Science · #Algebraic Geometry (math.AG) #Computability, Logic, AI Algorithms #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2506.20280

openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

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.

Citations

• Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension
• Bernstein-Sato polynomials for general ideals vs. principal ideals
• Spectrum and multiplier ideals of arbitrary subvarieties
• Bernstein-Sato polynomials of arbitrary varieties

Related

• Brieskorn modules and Gauss-Manin systems for non isolated hypersurface singularities
• Monodromy of Hypersurface Singularities
• Algebraic Gauss-Manin Systems and Brieskorn Modules
• Families of ICIS with constant total Milnor number
• Irregularity of an analogue of the Gauss-Manin systems