On the fundamental groups of normal varieties

TL;DR

This paper investigates the properties of fundamental groups of normal complex algebraic varieties, demonstrating their similarities to smooth varieties and exploring the relationship of jump loci with resolutions and smoothings.

Contribution

It establishes that the fundamental groups of normal varieties share key properties with smooth varieties and relates jump loci across different geometric modifications.

Findings

Fundamental groups of normal varieties exhibit properties similar to smooth varieties.

Jump loci of rank one local systems relate to those of resolutions and smoothings.

Provides new insights into the topology of normal algebraic varieties.

Abstract

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a resolution and of a smoothing of this variety.