Blow-ups for the Horn–Kapranov parametrization of the classical discriminant
Evgeny Mikhalkin
Siberian Federal University, Krasnoyarsk, Russian FederationVitaly Stepanenko
Siberian Federal University, Krasnoyarsk, Russian FederationAvgust Tsikh
Siberian Federal University, Krasnoyarsk, Russian Federation
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Abstract
The Horn–Kapranov parametrizations describe the singular sets of hypergeometric functions in several variables. These parametrizations are inverses of logarithmic Gauss maps for A-discriminants. In this paper we demonstrate that, despite the multivalued nature of the indicated parametrizations, their blow-ups properties are the same as for single-valued meromorphic mappings. As an application, a new proof of factorization identities for the classical discriminant is given.