Local systems on proper algebraic V-manifolds

TL;DR

This paper explores the topology of proper algebraic V-manifolds using coverings by smooth projective varieties and nonabelian Hodge theory, extending methods to Deligne-Mumford stacks and simplicial varieties.

Contribution

It introduces a novel approach combining coverings and nonabelian Hodge techniques to analyze the topology of algebraic stacks and simplicial varieties.

Findings

Topological insights into proper Deligne-Mumford stacks

Extension of nonabelian Hodge methods to stacks

New techniques for studying simplicial varieties

Abstract

We use coverings by smooth projective varieties then apply nonabelian Hodge techniques to study the topology of proper Deligne-Mumford stacks as well as more general simplicial varieties.