Calabi-Yau complete intersections associated to good pairs of generalized nef partitions

TL;DR

This paper introduces a new framework for describing Calabi-Yau complete intersections in Q-Fano toric varieties using good pairs of generalized nef partitions, extending mirror symmetry dualities.

Contribution

It defines good pairs of generalized nef partitions and a duality that generalizes Batyrev-Borisov and Berglund-H"ubsch-Krawitz dualities for Calabi-Yau varieties.

Findings

Introduces the concept of good pairs of generalized nef partitions.

Establishes a duality extending Batyrev-Borisov mirror symmetry.

Generalizes Berglund-H"ubsch-Krawitz duality to quasismooth complete intersections.

Abstract

We introduce the notion of good pair of generalized nef partitions to describe Calabi-Yau complete intersections in Q-Fano toric varieties whose equations do not necessarily have maximal Newton polytopes. Moreover, we define a natural duality between them which generalizes Batyrev-Borisov mirror duality and allows to define a generalization of Berglund-H\"ubsch-Krawitz duality to quasismooth complete intersections.