A Note on (0,2) Models on Calabi-Yau Complete Intersections

TL;DR

This paper explores additional degrees of freedom in resolving singularities in (0,2) heterotic compactifications, focusing on nef partitions of anticanonical divisors in Gorenstein Fano toric varieties, expanding the understanding of Calabi-Yau complete intersections.

Contribution

It introduces a new aspect of resolving singularities in (0,2) models through nef partitions, offering a novel perspective in the construction of Calabi-Yau varieties.

Findings

Identifies a new degree of freedom in resolving singularities.

Connects nef partitions to gauge bundle constructions.

Enhances understanding of (0,2) heterotic compactifications.

Abstract

In the class of (0,2) heterotic compactifications which has been constructed in the framework of gauged linear sigma models the Calabi-Yau varieties X are realized as complete intersections of hypersurfaces in toric varieties IP and the corresponding gauge bundles (or more generally gauge sheaves) E are defined by some short exact sequences. We show that there is yet another degree of freedom in resolving singularities in such models which is related to the possible choices of nef partitions of the anticanonical divisors in Gorenstein Fano toric varieties IP.