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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.