Dualities between K3 fibered Calabi-Yau three-folds

TL;DR

This paper explores dualities in Calabi-Yau three-folds by constructing and analyzing different toric representations, revealing relations among various phases and the presence of Del Pezzo 4-cycles in K3 fibered examples.

Contribution

It introduces a method to identify relations among Calabi-Yau three-folds via toric representations and examines their phases and fiber structures, advancing understanding of string dualities.

Findings

Multiple phases contain Del Pezzo 4-cycles in six different ways.

Examples with Hodge numbers (5,185) exhibit various K3 fiber structures.

Relations among different toric representations are established.

Abstract

We propose a way to examine N=1 and N=2 string dualities on Calabi-Yau three-folds or extensions. Our way is to find out or to construct two types of toric representations of a Calabi-Yau three-fold, which contain phases topologically equivalent or phases connected by flops. We discuss how to find relations among Calabi-Yau three-folds realized in different toric representations. We examine several examples of Calabi-Yau three-folds which have the Hodge numbers, $(h^{1,1},h^{2,1})=(5,185)$ and the various numbers of K3 fibers. We observe that each phase of our examples contains Del Pezzo 4-cycles, $B_8$ in six ways.