Monodromy at infinity of $A$-hypergeometric functions and toric compactifications

TL;DR

This paper investigates the monodromy at infinity of $A$-hypergeometric functions, providing a formula for eigenvalues of monodromy automorphisms using toric compactifications to analyze their analytic continuations.

Contribution

It introduces a new formula for monodromy eigenvalues of $A$-hypergeometric functions employing toric compactifications, advancing understanding of their asymptotic behavior.

Findings

Derived explicit eigenvalue formulas for monodromy automorphisms.

Applied toric compactifications to analyze hypergeometric functions at infinity.

Enhanced the theoretical framework for $A$-hypergeometric functions' monodromy analysis.

Abstract

We study $A$-hypergeometric functions introduced by Gelfand-Kapranov-Zelevinsky and prove a formula for the eigenvalues of their monodromy automorphisms defined by the analytic continuaions along large loops contained in complex lines parallel to the coordinate axes. A method of toric compactifications will be used to prove our main theorem.