Infinitesimal Torelli theorem for cyclic coverings of generalized flag varieties I

TL;DR

This paper proves an effective infinitesimal Torelli theorem for cyclic covers of generalized flag varieties G/P, where G is a simple algebraic group and P a maximal parabolic subgroup, advancing understanding of their deformation theory.

Contribution

It provides the first effective infinitesimal Torelli theorem for cyclic covers of G/P, extending classical results to a broader class of algebraic varieties.

Findings

Establishment of an effective infinitesimal Torelli theorem for these covers

New techniques for analyzing deformation spaces of cyclic covers

Enhanced understanding of the relationship between geometry and Hodge theory in this context

Abstract

We give an effective infinitesimal Torelli theorem for cyclic covers of G/P, where G is a simple algebraic group and P is a maximal parabolic subgroup.