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In this note we give a detailed proof of a result (sketched by TorstenEkedahl in a discussion with the first author several years ago), describingcomplex tori admitting a rigid group action and showing explicitly theirprojectivity and their structure in terms of CM-fields. In the appendix, jointwith Benoit Claudon, we show, using a method of Green-Voisin, that all groupactions on complex tori deform to projective ones.

Rigid Group Actions on Complex Tori are Projective (after Ekedahl)