Closed form expressions for Hodge numbers of complete intersection Calabi-Yau threefolds in toric varieties

TL;DR

This paper derives explicit formulas for Hodge numbers of Calabi-Yau threefolds in toric varieties using lattice point counts, facilitating easier computation of their topological invariants.

Contribution

It provides closed form expressions for Hodge numbers of Calabi-Yau threefolds in five-dimensional toric ambient spaces, extending to higher dimensions.

Findings

Closed form formulas for Hodge numbers involving lattice point counts

Applicable to Calabi-Yau threefolds in five-dimensional spaces

Potential extension to higher-dimensional complete intersections

Abstract

We use Batyrev-Borisov's formula for the generating function of stringy Hodge numbers of Calabi-Yau varieties realized as complete intersections in toric varieties in order to get closed form expressions for Hodge numbers of Calabi-Yau threefolds in five-dimensional ambient spaces. These expressions involve counts of lattice points on faces of associated Cayley polytopes. Using the same techniques, similar expressions may be obtained for higher dimensional varieties realized as complete intersections of two hypersurfaces.