Torelli problem for Calabi-Yau threefolds with GLSM description

Abstract

We construct a gauged linear sigma model with two non-birational Kälher 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.

Exposition improved, some arguments clarified