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- Title
On zero-dimensional linear sections of surfaces of maximal sectional regularity.
- Authors
Lee, Wanseok; Park, Euisung
- Abstract
Let X ⊂ ℙ r be an n -dimensional nondegenerate irreducible projective variety of degree d and codimension e. For 1 ≤ β ≤ e and a β -dimensional linear subspace L ⊂ ℙ r satisfying dim(X ∩ L) = 0 , ℓ β (X) is defined as the possibly maximal length of the scheme theoretic intersection X ∩ L. Then it is well known that ℓ 1 (X) ≤ d − e + 1 if X is a curve. Also it was generalized by Noma [Multisecant lines to projective varieties, Projective Varieties with Unexpected Properties (Walter de Gruyter, GmbH and KG, Berlin, 2005), pp. 349–359] that ℓ β (X) ≤ d − e + β for all 1 ≤ β ≤ e , when X is locally Cohen–Macaulary. On the other hand, the possible values of ℓ β (X) are unknown if X is not locally Cohen–Macaulay. In this paper, we construct surfaces S ⊂ ℙ 5 of maximal sectional regularity (which are not locally Cohen–Macaulay) and of degree d for every d ≥ 7 such that ℓ β (S) ≥ d − 3 + β + (β − 1) d 2 − 1 − 2 , for all β ∈ { 2 , 3 }.
- Subjects
BERLIN (Germany)
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 10, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502213