On multisecant planes of locally non-Cohen-Macaulay surfaces

Wanseok Lee, Euisung Park

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

For a nondegenerate projective irreducible variety X ⊂ Pr, it is a natural problem to find an upper bound for the value of ℓβ(X) = max{length(X ∩ L) | L = Pβ ⊂ Pr, dim (X ∩ L) = 0} for each 1 ≤ β ≤ e. When X is locally Cohen-Macaulay, A. Noma in [10] proves that ℓβ (X) is at most d − e + β where d and e are respectively the degree and the codimension of X. In this paper, we construct some surfaces S ⊂ P5 of degree d ∈ {7,..., 12} which satisfies the inequality (Formula Presented) This shows that Noma’s bound is no more valid for locally non-Cohen-Macaulay varieties.

Original languageEnglish
Pages (from-to)1323-1330
Number of pages8
JournalBulletin of the Korean Mathematical Society
Volume54
Issue number4
DOIs
Publication statusPublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Korean Mathematical Society.

Keywords

  • Locally Cohen-Macaulayness
  • Multisecant space
  • Rational surface

ASJC Scopus subject areas

  • General Mathematics

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