Generic Torelli with denominators for elliptic surfaces

TL;DR

This paper proves that a broad class of Jacobian elliptic surfaces can be uniquely identified by their polarized rational Hodge structures, under certain geometric constraints.

Contribution

It establishes a Torelli-type theorem for generic Jacobian elliptic surfaces with specific conditions, extending understanding of their Hodge-theoretic characterization.

Findings

Determined by polarized rational Hodge structure

Applicable to very general Jacobian elliptic surfaces

Subject to constraints on irregularity and geometric genus

Abstract

We show that a very general Jacobian elliptic surface is determined by its polarized rational Hodge structure, subject to various constraints on the irregularity and the geometric genus.