RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
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


Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 4, Pages 49–66 (Mi izv347)  

This article is cited in 1 scientific paper (total in 1 paper)

A'Campo–Gusein-Zade diagrams as partially ordered sets

G. G. Ilyuta

Independent University of Moscow

Abstract: The real analogues of many results about complex monodromies of singularities can be formulated and proved in terms of partial orderings on A'Campo–Gusein-Zade diagrams, the real versions of Coxeter–Dynkin diagrams of singularities. In this paper it is proved that the only diagrams among the A'Campo–Gusein-Zade diagrams of singularities that determine partially ordered sets of finite type (in the sense of representations of a quiver) are the diagrams of simple singularities. To encode the real decompositions of a singularity the analogue of Vasilev invariants turn out to be surjections of a partially ordered set onto a chain. Formulae are proved for Arnold $(\operatorname{mod}2)$-invariants of plane curves in terms of the corresponding A'Campo–Gusein-Zade diagrams. We define, in the context of higher Bruhat orders, higher partially ordered sets and we describe their connection with the higher $M$-Morsifications $A_n$. We also consider certain previously known results about real singularities from the point of view of partially ordered sets.

DOI: https://doi.org/10.4213/im347

Full text: PDF file (1902 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2001, 65:4, 687–704

Bibliographic databases:

MSC: 06A99
Received: 21.03.2000

Citation: G. G. Ilyuta, “A'Campo–Gusein-Zade diagrams as partially ordered sets”, Izv. RAN. Ser. Mat., 65:4 (2001), 49–66; Izv. Math., 65:4 (2001), 687–704

Citation in format AMSBIB
\Bibitem{Ily01}
\by G.~G.~Ilyuta
\paper A'Campo--Gusein-Zade diagrams as partially ordered sets
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 4
\pages 49--66
\mathnet{http://mi.mathnet.ru/izv347}
\crossref{https://doi.org/10.4213/im347}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1857710}
\zmath{https://zbmath.org/?q=an:1026.58031}
\elib{http://elibrary.ru/item.asp?id=13672138}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 4
\pages 687--704
\crossref{https://doi.org/10.1070/IM2001v065n04ABEH000347}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746837383}


Linking options:
  • http://mi.mathnet.ru/eng/izv347
  • https://doi.org/10.4213/im347
  • http://mi.mathnet.ru/eng/izv/v65/i4/p49

    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. G. G. Ilyuta, “Interpolation by symmetric functions and alternating higher Bruhat orders”, Izv. Math., 67:5 (2003), 849–880  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:453
    Full text:127
    References:62
    First page:3

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019