This article is cited in 8 papers

Singular strata of cuspidal type for the classical discriminant

E. N. Mikhalkin, A. K. Tsikh

Siberian Federal University, Krasnoyarsk

Abstract: We consider an algebraic equation with variable complex coefficients. For the reduced discriminant set of such an equation we obtain parametrizations of the singular strata corresponding to the existence of roots of multiplicity at least $j$. These parametrizations are the restrictions of the Horn-Kapranov parametrization of the whole discriminant set to a chain of nested linear subspaces of the projective space. It is proved that such strata can be transformed into reduced $A$-discriminant sets by monomial transformations.
Bibliography: 12 titles.

Keywords: general algebraic equation, $A$-discriminant set, Horn-Kapranov parametrization, singular stratum.

UDC: 512.761+517.55

MSC: Primary 14M25; Secondary 14J70

Received: 05.03.2014 and 30.09.2014

DOI: 10.4213/sm8355

 English version: Sbornik: Mathematics, 2015, 206:2, 282–310

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