L\^e modules and hypersurfaces with one-dimensional singular sets

TL;DR

This paper explores the cohomology of Milnor fibers and local systems of hypersurfaces with one-dimensional singularities, utilizing previous results on Lê modules and Betti number bounds to advance understanding of their topological properties.

Contribution

It introduces new insights into the cohomology of Milnor fibers for hypersurfaces with one-dimensional singular sets using Lê modules and Betti number bounds.

Findings

Established bounds on Betti numbers for these hypersurfaces

Analyzed the structure of local systems from vanishing cycles

Connected Lê modules to the topology of singular hypersurfaces

Abstract

By using our previous results on L\^e modules and an upper-bound on the betti numbers which we proved with L\^e, we investigate the cohomology of Milnor fibers and the internal local systems given by the vanishing cycles of hypersurfaces with one-dimensional singular sets and small L\^e numbers.