Rigid but not infinitesimally rigid compact complex manifolds

Abstract

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

21 pages, 2 figures. v2: exposition improved, some results in Section 2 proved in higher generality, proof of Lemma 5.2 simplified. Final version, to be published on Duke Math. J