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

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.

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

Bibliographic databases:

UDC: 512.7

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
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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
2. A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845
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