Communications in Number Theory and Physics

Volume 13 (2019)

Number 4

Torelli problem for Calabi–Yau threefolds with GLSM description

Pages: 725 – 761

DOI: https://dx.doi.org/10.4310/CNTP.2019.v13.n4.a2

Authors

Michał Kapustka (Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland; and Department of Mathematics and Natural Sciences, University of Stavanger, Norway)

Marco Rampazzo (Department of Mathematics and Natural Sciences, University of Stavanger, Norway)

Abstract

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

Keywords

Calabi–Yau manifolds, Fourier–Mukai pairs, derived equivalence, gauged linear sigma models, Torelli type problems

Full Text (PDF format)

M. Kapustka was supported by the project NCN 2013/10/E/ST1/00688.

M. Rampazzo was supported by the PhD program at the University of Stavanger.

Received 15 May 2018

Accepted 18 June 2019

Published 6 December 2019