Rigid but not infinitesimally rigid compact complex manifolds

TL;DR

This paper constructs an infinite series of rigid compact complex manifolds in each dimension greater than or equal to two, which are not infinitesimally rigid, resolving a longstanding problem in complex manifold theory.

Contribution

It provides explicit examples of rigid but not infinitesimally rigid compact complex manifolds, answering a key open question in the field.

Findings

Existence of infinite series of such manifolds in each dimension d ≥ 2

These manifolds are rigid but not infinitesimally rigid

Complete resolution of Morrow and Kodaira's problem

Abstract

In this paper the authors give an infinite series of rigid compact complex manifolds for each dimension $d \geq 2$ which are not infinitesimally rigid, hence giving a complete answer to a problem of Morrow and Kodaira stated in the famous book "Complex manifolds".