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 language | English |
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Pages (from-to) | 1323-1330 |
Number of pages | 8 |
Journal | Bulletin of the Korean Mathematical Society |
Volume | 54 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Locally Cohen-Macaulayness
- Multisecant space
- Rational surface
ASJC Scopus subject areas
- Mathematics(all)