A-hypergeometric series and the Hasse-Witt matrix of a hypersurface

TL;DR

This paper provides a combinatorial proof of the invertibility of the Hasse-Witt matrix for hypersurfaces and explores its connection to A-hypergeometric series, advancing understanding of algebraic geometry in characteristic p.

Contribution

It introduces a new combinatorial proof for the invertibility of the Hasse-Witt matrix and investigates its relationship with A-hypergeometric series.

Findings

Proves generic invertibility of the Hasse-Witt matrix

Establishes a link between the Hasse-Witt matrix and A-hypergeometric series

Provides insights into the structure of hypersurfaces in characteristic p

Abstract

We give a short combinatorial proof of the generic invertibility of the Hasse-Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse-Witt matrix and certain $A$-hypergeometric series, which is what motivated the proof.