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This article is cited in 15 scientific papers (total in 15 papers)
The discriminant locus of a system of $n$ Laurent polynomials in $n$ variables
I. A. Antipovaa, A. K. Tsikhb a Institute of Space and Information Technologies, Siberian Federal University
b Institute of Mathematics, Siberian Federal University
Abstract:
We consider a system of $n$ algebraic equations in $n$ variables, where
the exponents of the monomials in each equation are fixed while all the
coefficients vary. The discriminant locus of such a system is
the closure of the set of all coefficients for which the system has
multiple roots with non-zero coordinates. For dehomogenized discriminant loci,
we give parametrizations of those irreducible components that depend
on the coefficients of all the equations. We prove that if such a component
has codimension 1, then the parametrization is inverse to the logarithmic
Gauss map of the component (an analogue of Kapranov's result for the
$A$-discriminant). Our argument is based on the linearization of algebraic
systems and the parametrization of the set of its critical values.
Keywords:
discriminant locus, linearization of an algebraic system, logarithmic Gauss map.
Received: 03.02.2011 Revised: 21.11.2011
Citation:
I. A. Antipova, A. K. Tsikh, “The discriminant locus of a system of $n$ Laurent polynomials in $n$ variables”, Izv. RAN. Ser. Mat., 76:5 (2012), 29–56; Izv. Math., 76:5 (2012), 881–906
Linking options:
https://www.mathnet.ru/eng/im6990https://doi.org/10.1070/IM2012v076n05ABEH002608 https://www.mathnet.ru/eng/im/v76/i5/p29
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Abstract page: | 1169 | Russian version PDF: | 527 | English version PDF: | 51 | References: | 68 | First page: | 36 |
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