A-hypergeometric functions in transcendental questions of algebraic geometry

TL;DR

This paper extends the theory of A-hypergeometric functions by demonstrating that periods of middle dimension on complex algebraic varieties are expressible as these functions, linking algebraic geometry and special functions.

Contribution

The authors generalize the construction of A-hypergeometric functions, showing their relation to periods of algebraic varieties, which was not previously established.

Findings

Periods of middle dimension are A-hypergeometric functions.

A-hypergeometric functions relate to polynomial coefficients of algebraic varieties.

The work broadens the application of A-hypergeometric functions in algebraic geometry.

Abstract

We generalize the known constructions of A-hypergeometric functions. In particular, we show that periods of middle dimension on affine or projective complex algebraic varieties are A-hypergeometric functions of coefficients of polynomial equations of these varieties.