Brief communications

$A$-Hypergeometric Functions in Transcendental Questions of Algebraic Geometry

A. V. Stoyanovskii

Russian State University for the Humanities, Moscow

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

Keywords: hypergeometric system, periods, Gelfand–Leray integral.

UDC: 517.95

Received: 17.04.2012

DOI: 10.4213/faa3135

 English version: Functional Analysis and Its Applications, 2014, 48:1, 76–78

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