Correspondences between modular Calabi--Yau fiber products

TL;DR

This paper introduces methods to construct rational morphisms and correspondences between fiber products of rational elliptic surfaces and certain Calabi--Yau threefolds, enriching the understanding of their geometric relationships.

Contribution

It presents two novel approaches for creating finite rational morphisms and correspondences between fiber products of rational elliptic surfaces and rigid Calabi--Yau threefolds.

Findings

Constructed rational morphisms between fiber products and Calabi--Yau manifolds.

Established correspondences for fiber products with up to five singular fibers.

Enhanced understanding of geometric relations among Calabi--Yau threefolds.

Abstract

We describe two ways to construct finite rational morphisms between fiber products of rational elliptic surfaces with section and some Calabi--Yau manifolds. We use them to construct correspondences between such fiber products that admit at most five singular fibers and rigid Calabi--Yau threefolds.