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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 4, Pages 82–94 (Mi faa3044)  

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

Intersection theory and Hilbert function

A. G. Khovanskiiabc

a The University of Toronto, Toronto, Canada
b Institute of Systems Analysis of Russian Academy of Sciences
c Independent University of Moscow

Abstract: Birationally invariant intersection theory is a far-reaching generalization and extension of the Bernstein–Kushnirenko theorem. This paper presents transparent proofs of Hilbert's theorem on the degree of a projective variety and other related statements playing an important role in this theory. The paper is completely self-contained; we recall all necessary definitions and statements.

Keywords: degree of projective variety, Hilbert function, intersection theory, Bernstein–Kushnirenko theorem.

DOI: https://doi.org/10.4213/faa3044

Full text: PDF file (228 kB)
References: PDF file   HTML file

English version:
Functional Analysis and Its Applications, 2011, 45:4, 305–315

Bibliographic databases:

Document Type: Article
UDC: 512.761+515.171.3
Received: 07.12.2010

Citation: A. G. Khovanskii, “Intersection theory and Hilbert function”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 82–94; Funct. Anal. Appl., 45:4 (2011), 305–315

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/faa3044
  • https://doi.org/10.4213/faa3044
  • http://mi.mathnet.ru/eng/faa/v45/i4/p82

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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. Kaveh K., Khovanskii A.G., “Newton-Okounkov bodies, semigroups of integral points, graded algebras and intersection theory”, Ann. of Math. (2), 176:2 (2012), 925–978  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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