Birationality and Landau-Ginzburg models

TL;DR

This paper introduces a new technique to address birationality questions in mirror symmetry, confirming the birationality of Calabi-Yau families linked to multiple mirror nef-partitions, advancing understanding in the field.

Contribution

It presents a novel approach to birationality in mirror symmetry and resolves a longstanding question about Calabi-Yau families and nef-partitions.

Findings

Confirmed birationality of Calabi-Yau families for multiple mirror nef-partitions

Provided new insights into Borisov's nef-partitions

Advanced the understanding of the multiple mirror phenomenon

Abstract

We introduce a new technique for approaching birationality questions that arise in the mirror symmetry of complete intersections in toric varieties. As an application we answer affirmatively and conclusively the question of Batyrev-Nill (2008) about the birationality of Calabi-Yau families associated to multiple mirror nef-partitions. This completes the progress in this direction made by Li's breakthrough (2016). In the process, we obtain results in the theory of Borisov's nef-partitions (1993) and provide new insight on the geometric content of the multiple mirror phenomenon.