An Index Theorem for Modules on a Hypersurface Singularity

TL;DR

This paper provides a topological interpretation of Hochster's Theta pairing for modules on hypersurface rings, generalizing previous results and confirming a conjecture about its vanishing in certain singularities.

Contribution

It introduces a topological perspective on Hochster's Theta pairing, extending known results and proving a conjecture related to hypersurface singularities.

Findings

Theta pairing expressed via linking numbers

Generalization of Hochster's results

Proof of Steenbrink's conjecture

Abstract

A topological interpretation of Hochster's Theta pairing of two modules on a hypersurface ring is given in terms of linking numbers. This generalizes results of M. Hochster and proves a conjecture of J. Steenbrink. As a corollary we get that the Theta pairing vanishes for isolated hypersurface singularities in an odd number of variables, as was conjectured by H. Dao.