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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2012, Volume 276, Pages 239–254 (Mi tm3372)  

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

On the multiplicity of solutions of a system of algebraic equations

A. V. Pukhlikovab

a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
b University of Liverpool, Liverpool, UK

Abstract: We obtain upper bounds for the multiplicity of an isolated solution of a system of equations $f_1=…=f_M=0$ in $M$ variables, where the set of polynomials $(f_1,…,f_M)$ is a tuple of general position in a subvariety of a given codimension which does not exceed $M$, in the space of tuples of polynomials. It is proved that as $M\to\infty$ this multiplicity grows no faster than $\sqrt M\exp[\omega\sqrt M]$, where $\omega>0$ is a certain constant.

Full text: PDF file (229 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 276, 234–249

Bibliographic databases:

UDC: 512.7
Received in August 2011

Citation: A. V. Pukhlikov, “On the multiplicity of solutions of a system of algebraic equations”, Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Tr. Mat. Inst. Steklova, 276, MAIK Nauka/Interperiodica, Moscow, 2012, 239–254; Proc. Steklov Inst. Math., 276 (2012), 234–249

Citation in format AMSBIB
\Bibitem{Puk12}
\by A.~V.~Pukhlikov
\paper On the multiplicity of solutions of a~system of algebraic equations
\inbook Number theory, algebra, and analysis
\bookinfo Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 276
\pages 239--254
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3372}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2986124}
\elib{http://elibrary.ru/item.asp?id=17680283}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 276
\pages 234--249
\crossref{https://doi.org/10.1134/S0081543812010208}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303468300020}
\elib{http://elibrary.ru/item.asp?id=17983889}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84860362313}


Linking options:
  • http://mi.mathnet.ru/eng/tm3372
  • http://mi.mathnet.ru/eng/tm/v276/p239

    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. Pukhlikov A.V., “Birational Rigidity of Fano Complete Intersections”, Dokl. Math., 87:1 (2013), 34–35  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:148
    Full text:15
    References:31

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