Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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. Math., 76:5 (2012), 881–906
Citation in format AMSBIB
\Bibitem{AntTsi12}
\by I.~A.~Antipova, A.~K.~Tsikh
\paper The discriminant locus of a~system of $n$ Laurent polynomials in $n$ variables
\jour Izv. Math.
\yr 2012
\vol 76
\issue 5
\pages 881--906
\mathnet{http://mi.mathnet.ru//eng/im6990}
\crossref{https://doi.org/10.1070/IM2012v076n05ABEH002608}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3024862}
\zmath{https://zbmath.org/?q=an:1254.32012}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000310548800002}
\elib{https://elibrary.ru/item.asp?id=20359146}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84868114072}
Linking options:
  • https://www.mathnet.ru/eng/im6990
  • 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
    Statistics & downloads:
    Abstract page:1171
    Russian version PDF:527
    English version PDF:52
    References:68
    First page:36
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024