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Izvestiya: Mathematics, 2012, Volume 76, Issue 5, Pages 881–906
DOI: https://doi.org/10.1070/IM2012v076n05ABEH002608
(Mi im6990)
 

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
References:
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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2012, Volume 76, Issue 5, Pages 29–56
DOI: https://doi.org/10.4213/im6990
Bibliographic databases:
Document Type: Article
UDC: 517.55+512.7
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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\paper The discriminant locus of a~system of $n$ Laurent polynomials in $n$ variables
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\issue 5
\pages 29--56
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\jour Izv. Math.
\yr 2012
\vol 76
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\pages 881--906
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  • https://doi.org/10.1070/IM2012v076n05ABEH002608
  • https://www.mathnet.ru/eng/im/v76/i5/p29
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1169
    Russian version PDF:527
    English version PDF:51
    References:68
    First page:36
     
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