On multisecant planes of locally non-Cohen-Macaulay surfaces

Wanseok Lee, Euisung Park

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    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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