Rigid manifolds of general type with non-contractible universal cover

Abstract

For each $$n\ge 3$$ n ≥ 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.

Some surfaces with canonical maps of degrees 10, 11, and 14

“…Recently, similar constructions involving non‐free actions on a product of Fermat curves have been used to provide other interesting projective manifolds that helped us to understand some important geometric phenomena. Most notably are the rigid but not infinitesimally rigid manifolds [4] of Bauer and Pignatelli that gave a negative answer to a question of Kodaira and Morrow [11, p. 45] and, to a lesser degree, also the infinite series of n ‐dimensional infinitesimally rigid manifolds of general type with non‐contractible universal cover for each $$n\ge 3$$, provided by Frapporti and the second author of this paper [8].…”