Boundedness of the Images of Period Maps

TL;DR

This paper proves Griffiths' conjecture that the image of the lifted period map on the universal cover is contained within a bounded domain in complex Euclidean space, advancing understanding of period maps in Hodge theory.

Contribution

It establishes the boundedness of the image of the lifted period map, confirming a key conjecture in the theory of period maps and Hodge structures.

Findings

The image of the lifted period map is bounded in complex Euclidean space.

The conjecture of Griffiths on simultaneous normalization is proven.

The result enhances the understanding of the geometry of period domains.

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 complex Euclidean space.