Torelli problem for Calabi-Yau threefolds with GLSM description

TL;DR

This paper constructs a GLSM with two non-birational phases that are shown to be derived, L-, deformation, and Hodge equivalent, providing a counterexample to the birational Torelli problem.

Contribution

It introduces a new counterexample to the birational Torelli problem using a GLSM with two non-birational phases that are equivalently derived and Hodge related.

Findings

Two non-birational phases are derived equivalent.

The phases are L- and deformation equivalent.

The phases are Hodge equivalent.

Abstract

We construct a gauged linear sigma model with two non-birational K\"alher phases which we prove to be derived equivalent, $\mathbb{L}$-equivalent, deformation equivalent and Hodge equivalent. This provides a new counterexample to the birational Torelli problem which admits a simple GLSM interpretation.