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Singularities of hypergeometric functions in several variables

Published online by Cambridge University Press:  21 April 2005

Mikael Passare ,
Timur Sadykov  and
August Tsikh
Mikael Passare
Affiliation:
Department of Mathematics, University of Stockholm, SE-10691 Stockholm, Swedenpassare@math.su.se
Timur Sadykov
Affiliation:
Department of Mathematics, Krasnoyarsk State University, 660041 Krasnoyarsk, Russiasadykov@lan.krasu.ru
August Tsikh
Affiliation:
Department of Mathematics, Krasnoyarsk State University, 660041 Krasnoyarsk, Russiatsikh@lan.krasu.ru
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Abstract

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This paper deals with singularities of nonconfluent hypergeometric functions in several complex variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such hypersurfaces in terms of the amoebas and the Newton polytopes of their defining polynomials. In particular, we show that the amoebas of classical discriminantal hypersurfaces are solid, that is, they possess the minimal number of complement components.

Keywords

hypergeometric functionsamoebasNewton polytopes32A0532A2033C70
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 3 , May 2005 , pp. 787 - 810
Copyright
Foundation Compositio Mathematica 2005