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

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

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

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{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746837383} 

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

 SHARE:

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
•  Number of views: This page: 521 Full text: 169 References: 65 First page: 3