Blow-ups for the Horn–Kapranov parametrization of the classical discriminant

  • Evgeny Mikhalkin

    Siberian Federal University, Krasnoyarsk, Russian Federation
  • Vitaly Stepanenko

    Siberian Federal University, Krasnoyarsk, Russian Federation
  • Avgust Tsikh

    Siberian Federal University, Krasnoyarsk, Russian Federation
Blow-ups for the Horn–Kapranov parametrization of the classical discriminant cover
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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.