Linear Shafarevich Conjecture

TL;DR

This paper proves that for complex projective manifolds with linear fundamental groups, their universal covers are holomorphically convex, advancing understanding of the relationship between fundamental groups and complex geometry.

Contribution

It establishes a new link between linear fundamental groups and the holomorphic convexity of universal covers in complex geometry.

Findings

Universal covers are holomorphically convex when fundamental groups are linear

Supports conjectures relating algebraic properties of groups to complex geometric structures

Provides new tools for studying the geometry of complex projective manifolds

Abstract

We prove that the universal covering space of a complex projective manifold is holomorphically convex provided its fundamental group is linear.