The deletion restriction method for plane curve germ complement

TL;DR

This paper investigates the cohomology jump loci of rank one local systems in plane curve germ complements using the deletion restriction method, revealing that results depend solely on linking numbers between components.

Contribution

Introduces a deletion restriction approach to analyze cohomology jump loci, emphasizing the role of linking numbers in plane curve germ complements.

Findings

Results depend only on linking numbers between components.

Deletion restriction method simplifies the analysis of cohomology jump loci.

Provides new insights into the topology of plane curve germ complements.

Abstract

We study the cohomology jump loci of rank one local systems for the plane curve germ complement by the deletion restriction method. In particular, the deletion restriction type results in this case only depend on the linking numbers between the irreducible components of the plane curve germ.