On ampleness of canonical bundle

TL;DR

This paper explores the properties of projective manifolds with specific fundamental groups, extending classical theorems to broader contexts and providing new insights into their geometric structure.

Contribution

It generalizes the uniformization theorem and Maltsev's theorem to manifolds with nonamenable, non-residually finite fundamental groups.

Findings

Extended uniformization theorem to new classes of manifolds

Generalized Maltsev's theorem for specific subgroup types

Provided new geometric insights into fundamental groups

Abstract

We study projective manifolds with nonamenable and non-residually finite fundamental groups. We generalize the uniformization theorem of our earlier note. We generalize a classical theorem of Maltsev about finitely generated subgroups of GL(m).