On K3 fibered Calabi-Yau 3-folds

TL;DR

This paper explores K3 fibered Calabi-Yau 3-folds, establishing dual fibrations that are derived equivalent and relating these structures to mirror symmetry, advancing understanding of their geometric and categorical properties.

Contribution

It introduces a dual fibration construction for K3 fibered Calabi-Yau 3-folds and connects it to mirror symmetry and derived equivalences.

Findings

Dual fibrations are derived equivalent to the original

The dual fibration relates to mirror symmetry

Provides new insights into the moduli of semistable sheaves

Abstract

Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain a dual fibration that turns to be derived equivalent to the original one and we relate the problem to mirror symmetry.