Remarks on eigenspectra of isolated singularities

TL;DR

This paper develops a new calculus to analyze Hodge-theoretic invariants of isolated singularities with automorphisms, providing explicit computations and applications to singularity bounds and monodromy in variations of Hodge structures.

Contribution

It introduces a simple calculus extending Steenbrink spectrum for describing invariants of singularities with automorphisms, including explicit eigenspectra computations and applications.

Findings

Computed eigenspectra for quasi-homogeneous singularities

Applied eigenspectra to bounds on singularities

Analyzed monodromy of variations of Hodge structures

Abstract

We introduce a simple calculus, extending a variant of the Steenbrink spectrum, for describing Hodge-theoretic invariants of (smoothings of) isolated singularities with (relative) automorphisms. After computing these "eigenspectra" in the quasi-homogeneous case, we give three applications to singularity bounding and monodromy of VHS.