Rigid group actions on complex tori are projective (after Ekedahl)

In this paper, we give a detailed proof of a result due to Torsten Ekedahl, describing complex tori admitting a rigid group action and showing explicitly their projectivity and their structure in terms of CM-fields. In the appendix, joint with Claudon, we show, using a method of Green-Voisin, that all group actions on complex tori deform to projective ones. </jats:p

The classification of rigid hyperelliptic fourfolds

We provide a fine classification of rigid hyperelliptic manifolds in dimension four up to biholomorphism and diffeomorphism. These manifolds are explicitly described as finite étale quotients of a product of four Fermat elliptic curves