Rigid Manifolds of general type with non-contractible universal cover

TL;DR

This paper constructs examples of high-dimensional, infinitesimally rigid projective manifolds of general type that have non-contractible universal covers, including both projective and non-projective cases.

Contribution

It introduces new examples of rigid manifolds of general type with non-contractible universal covers across various dimensions and types.

Findings

Existence of infinitesimally rigid manifolds in all dimensions n ≥ 3.

Examples include both projective and non-projective universal covers.

Manifolds exhibit non-contractible universal covers.

Abstract

For each $n\geq 3$ we give examples of infinitesimally rigid projective manifolds of general type of dimension $n$ with non-contractible universal cover. We provide examples with projective and examples with non-projective universal cover.