Boundedness of the images of period maps and applications

Abstract

We prove a conjecture of Griffiths on simultaneous normalization of all periods which asserts that the image of the lifted period map on the universal cover lies in a bounded domain in a complex Euclidean space. As an application we prove that the Teichmüller spaces of a large class of projective 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