Counting Points and Hilbert Series in String Theory

TL;DR

This paper explores counting points in reflexive 4-dimensional polytopes and computes the Hilbert series for a vast class of these polytopes, linking combinatorial geometry with string theory applications.

Contribution

It introduces a method for counting points in reflexive 4-polytopes and computes their Hilbert series, providing new data for Calabi-Yau hypersurfaces in string theory.

Findings

Computed Hilbert series for 473,800,776 reflexive polytopes

Established connections between polytope counting and string theory models

Provided a comprehensive dataset for Calabi-Yau hypersurfaces

Abstract

The problem of counting points is revisited from the perspective of reflexive 4-dimensional polytopes. As an application, the Hilbert series of the 473,800,776 reflexive polytopes (equivalently, their Calabi-Yau hypersurfaces) are computed.