Picard Groups of Hypersurfaces in Toric Varieties

TL;DR

This paper investigates the structure of rational Picard groups of hypersurfaces in toric varieties, providing explicit combinatorial descriptions and exploring applications to Calabi-Yau spaces.

Contribution

It introduces a method to explicitly describe Picard groups of hypersurfaces in toric varieties using fan combinatorics, with applications to Calabi-Yau spaces.

Findings

Explicit basis of Picard group described via combinatorial data

Application framework for Calabi-Yau hypersurfaces

Enhanced understanding of hypersurface line bundles in toric geometry

Abstract

We study the structure of rational Picard groups of hypersurfaces of toric varieties. By using the fan structure associated to the ambient toric variety, an explicit basis of the Picard group is described by certain combinatorial data. We shall also discuss the application to Calabi-Yau spaces.