Moduli of Linear Sections of a General Hypersurface

TL;DR

This paper studies how the moduli of linear sections of a general hypersurface vary globally, proving a generic Torelli result and providing a comprehensive understanding of the moduli of line slices.

Contribution

It establishes a generic Torelli theorem for linear sections and characterizes the global variation of their moduli for general hypersurfaces.

Findings

Proves a generic Torelli theorem for linear sections.

Provides a complete description of the moduli variation.

Identifies conditions under which the moduli are uniquely determined.

Abstract

We investigate the global variation of moduli of linear sections of a general hypersurface. We prove a "generic Torelli" result for a large proportion of cases, and we obtain a complete picture of the global variation of moduli of line slices of a general hypersurface.