Generic Torelli and local Schottky theorems for Jacobian elliptic surfaces

TL;DR

This paper establishes a generic Torelli theorem for Jacobian elliptic surfaces, showing that the base curve can be recovered from period data when the geometric genus is sufficiently large relative to irregularity.

Contribution

It provides a new Torelli theorem for Jacobian elliptic surfaces and demonstrates how to recover the base curve from period data under certain conditions.

Findings

Proves a generic Torelli theorem for Jacobian elliptic surfaces.

Shows that the base curve can be recovered from period data.

Provides effective methods to determine defining equations from periods.

Abstract

We prove a generic Torelli theorem for Jacobian elliptic surfaces, provided that the geometric genus is large compared to the irregularity. The result is effective to the extent that defining equations for the base curve are recovered from the period data.