Algebraic correspondences between genus three curves and certain Calabi-Yau varieties

TL;DR

This paper establishes algebraic correspondences linking genus three curves to specific Calabi-Yau threefolds, revealing new insights into their cohomological structures and Hodge theory relationships.

Contribution

It constructs explicit algebraic correspondences between genus three curves and Calabi-Yau threefolds, and analyzes their Hodge structure interactions.

Findings

Cohomology groups of curves embed into those of Calabi-Yau threefolds.

The cokernel of the Hodge structure inclusion cannot arise from polarized abelian schemes.

Provides a new perspective on the Hodge theoretic properties of these geometric objects.

Abstract

In this paper, we construct certain algebraic correspondences between genus three curves and certain type of Calabi-Yau threefolds which is double coverings of three dimensional projective space. Via this correspondences, the first cohomology groups of the curves can be embedded into the third cohomology groups of the Calabi-Yau three folds. Moreover we prove that the cokernel of this inclusion of variations ofHodge structures can not be a factor of any variations of Hodge structures comming from polarized abelian schemes.