Intersection theory and Hilbert function

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...

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Bibliographic Details
Published inFunctional analysis and its applications Vol. 45; no. 4; pp. 305 - 315
Main Author Khovanskii, A. G.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.12.2011
Subjects
Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Hilbert function
Bernstein-Kushnirenko theorem
intersection theory
degree of projective variety
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Summary: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.
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-011-0033-6