A formula for Euler characteristic of line singularities on singular spaces

TL;DR

This paper derives an algebraic formula for calculating the Euler characteristic of Milnor fibers associated with functions having a smooth critical locus on weighted homogeneous complete intersection singular spaces.

Contribution

It introduces a new algebraic formula specifically for Euler characteristics of Milnor fibers in the context of singular spaces with smooth critical loci.

Findings

Derived an explicit algebraic formula for Euler characteristics

Applicable to weighted homogeneous complete intersections

Enhances understanding of singularity invariants

Abstract

We prove an algebraic formula for the Euler characteristic of the Milnor fibres of functions with critical locus a smooth curve on a space which is a weighted homogeneous complete intersection with isolated singularity.