Singularities of Nonconfluent Hypergeometric Functions in Several Variables

Details Singularities of Nonconfluent Hypergeometric Functions in Several Variables Singularities of Nonconfluent Hypergeometric Functions in Several Variables

2004-05-13

arxiv.org/abs/math/0405259v1

Mathematics

Complex Variables

30 pages, 7 figures

Scientific paper

The paper deals with singularities of nonconfluent hypergeometric functions in several variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We describe such hypersurfaces in terms of amoebas and the Newton polytopes of their defining polynomials. In particular, we show that all $\mathcal{A}$-discriminantal hypersurfaces (in the sense of Gelfand, Kapranov and Zelevinsky) have solid amoebas, that is, amoebas with the minimal number of complement components.

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