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On Horn-Kapranov uniformisation of the discriminantal loci. (English) Zbl 1222.14105
Brasselet, Jean-Paul (ed.) et al., Singularities in geometry and topology 2004. Proceedings of the 3rd Franco-Japanese colloquium on singularities, Hokkaido, Japan, September 13–18, 2004. Tokyo: Mathematical Society of Japan (ISBN 978-4-931469-39-6/hbk). Advanced Studies in Pure Mathematics 46, 223-249 (2007).
The author proves a rational parametrization equation of the discriminant loci associated to a nondegenerate affine complete intersection variety. To this end a relation of the fibre-integral with the Horn hypergeometric function and that of Gel’fand–Kapranov–Zelevinsky is established.
For the entire collection see [Zbl 1111.58001].

##### MSC:
 14M10 Complete intersections 55R80 Discriminantal varieties and configuration spaces in algebraic topology 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects) 33C65 Appell, Horn and Lauricella functions
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