RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mosc. Math. J.:
Year:
Volume:
Issue:
Page:
Find






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


Mosc. Math. J., 2006, Volume 6, Number 1, Pages 107–117 (Mi mmj238)  

This article is cited in 2 scientific papers (total in 2 papers)

Logarithmic vector fields for the discriminants of composite functions

V. V. Goryunov

Department of Mathematical Sciences, University of Liverpool

Abstract: The $K_f$-equivalence is a natural equivalence between map-germs $\varphi\mathbb C^m\mathbb C^n$ which ensures that their compositions $f\circ\varphi$ with a fixed function-germ f on $\mathbb C^n$ are the same up to biholomorphisms of $\mathbb C^m$. We show that the discriminant $\sum$ in the base of a $K_f$-versal deformation of a germ $\varphi$ is Saito's free divisor provided the critical locus of f is Cohen–Macaulay of codimension $m+1$ and all the transversal types of $f$ are $A_k$ singularities. We give an algorithm to construct basic vector fields tangent to $\sum$. This is a generalisation of classical Zakalyukin's algorithm to write out basic fields tangent to the discriminant of an isolated function singularity. The case of symmetric matrix families in two variables is done in detail. For simple singularities, it is directly related to Arnold's convolution of invariants of Weyl groups.

Key words and phrases: Logarithmic vector field, discriminant, composite function, free divisor, matrix singularities.

DOI: https://doi.org/10.17323/1609-4514-2006-6-1-107-117

Full text: http://www.ams.org/.../abst6-1-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 32S05; Secondary 58K20
Received: February 6, 2006
Language:

Citation: V. V. Goryunov, “Logarithmic vector fields for the discriminants of composite functions”, Mosc. Math. J., 6:1 (2006), 107–117

Citation in format AMSBIB
\Bibitem{Gor06}
\by V.~V.~Goryunov
\paper Logarithmic vector fields for the discriminants of composite functions
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 1
\pages 107--117
\mathnet{http://mi.mathnet.ru/mmj238}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-1-107-117}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265950}
\zmath{https://zbmath.org/?q=an:1121.58028}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595700007}


Linking options:
  • http://mi.mathnet.ru/eng/mmj238
  • http://mi.mathnet.ru/eng/mmj/v6/i1/p107

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Goryunov V.V., Zakalyukin V.M., “Lagrangian and legendrian varieties and stability of their projections”, Singularities in Geometry and Topology, 2005, 2007, 328–353  crossref  mathscinet  zmath  isi
    2. Miranda-Neto C.B., “A Module-Theoretic Characterization of Algebraic Hypersurfaces”, Can. Math. Bul.-Bul. Can. Math., 61:1 (2018), 166–173  crossref  mathscinet  zmath  isi
  • Moscow Mathematical Journal
    Number of views:
    This page:165
    References:60

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020