Hodge ideals for the determinant hypersurface

On Hodge Spectrum and Multiplier Ideals

We describe a relation between two invariants that measure the complexity of a hypersurface singularity. One is the Hodge spectrum which is related to the monodromy and the Hodge filtration on the cohomology of the Milnor fiber. The other is the multiplier ideal, having to do with log resolutions.

MULTIPLIER IDEALS, b-FUNCTION, AND SPECTRUM OF A HYPERSURFACE SINGULARITY

We prove that certain roots of the Bernstein-Sato polynomial (i.e. b-function) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain roots are determined by a filtration on the Milnor cohomology, generalizing a theorem of B. Malgrange in the isolated singularity case. This implies a certain...

Mixed Hodge structure in the cohomology of the Milnor fiber of a hypersurface singularity

I am only trying to make sense of Varchenko’s constructions.

Hodge structure of fibre integrals associated to the affine hypersurface in a torus

Abstract. We calculate the fibre integrals of the affine hypersurface in a torus in the form of their Mellin transforms. Especially, our method works efficiently for an affine hypersurface defined by a so called “simpliciable” polynomial. The relations between poles of Mellin transforms of fibre integrals, the mixed Hodge structure of the cohomology of the hypersruface, the hypergeometric diffe...

Algorithmic Gauss-Manin Connection Algorithms to Compute Hodge-theoretic Invariants of Isolated Hypersurface Singularities