The weights of isolated curve singularities are determined by Hodge ideals

Yang Wang, Stephen S.-T. Yau and Huaiqing Zuo

Vol. 334 (2025), No. 2, 349–376

DOI: 10.2140/pjm.2025.334.349

Abstract

We calculate Hodge ideals and Hodge moduli algebras for three types of isolated quasihomogeneous curve singularities. We show that Hodge ideals and Hodge moduli algebras of the singularities can determine the weights of the polynomials defining the singularities. We give some examples to explain why Hodge moduli algebras and the Hodge moduli sequence are better invariants than the characteristic polynomial (a topological invariant of the singularity) for nondegenerate quasihomogeneous singularities, in the sense that the characteristic polynomial cannot determine the weight type of the singularity.

Keywords

Hodge ideals, Hodge moduli algebras, Hodge moduli sequence, weight type, isolated quasihomogeneous curve singularities

Mathematical Subject Classification

Primary: 14B05, 32S05

Milestones

Received: 28 June 2024

Revised: 5 November 2024

Accepted: 1 February 2025

Published: 19 March 2025