Simultaneous normalization of period map and affine structures on moduli spaces

Abstract

We prove that the image of the lifted period map on the universal cover lies in a complex Euclidean space. We also prove that the Teichmüller spaces of a class of polarized manifolds have complex affine structures.

The original proof in this paper contains an error. A corrected version has been posted separately as arXiv:2602.13947. This withdrawal is made to prevent confusion and to direct readers to the revised paper