Quadratic forms for a 1-form on an isolated complete intersection singularity

Abstract

We consider a holomorphic 1-form $\omega$ with an isolated zero on an isolated complete intersection singularity $(V,0)$. We construct quadratic forms on an algebra of functions and on a module of differential forms associated to the pair $(V,\omega )$. They generalize the Eisenbud-Levine-Khimshiashvili quadratic form defined for a smooth $V$.