On hypersurfaces containing projective varieties

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Classical Castelnuovo's lemma shows that the number of linearly independent quadratic equations of a nondegenerate irreducible projective variety of codimension c is at most {c+12} and the equality is attained if and only if the variety is of minimal degree. Also a generalization of Castelnuovo's lemma by G. Fano implies that the next case occurs if and only if the variety is a del Pezzo variety. For curve case, these results are extended to equations of arbitrary degree respectively by J. Harris and S. L'vovsky. This paper is intended to extend these results to arbitrary dimensional varieties and to the next cases.

Original languageEnglish
Pages (from-to)843-875
Number of pages33
JournalForum Mathematicum
Volume27
Issue number2
DOIs
Publication statusPublished - 2015 Mar 1

Fingerprint

Projective Variety
Hypersurface
Lemma
If and only if
Quadratic equation
del operator
Arbitrary
Codimension
Equality
Linearly
Imply
Curve
Generalization

Keywords

  • Hilbert function
  • projective varieties of low degree

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On hypersurfaces containing projective varieties. / Park, Euisung.

In: Forum Mathematicum, Vol. 27, No. 2, 01.03.2015, p. 843-875.

Research output: Contribution to journalArticle

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