ON MULTISECANT PLANES OF LOCALLY NON-COHEN-MACAULAY SURFACES

Abstract

For a nondegenerate projective irreducible variety X subset of P-r, it is a natural problem to find an upper bound for the value of l(beta)(X) = max{length(X boolean AND L) | L = P-beta subset of P-r, dim (X boolean AND L) = 0} for each 1 <= beta <= e. When X is locally Cohen-Macaulay, A. Noma in [10] proves that l(beta) (X) is at most d - e + beta where d and e are respectively the degree and the codimension of X. In this paper, we construct some surfaces S subset of P-5 of degree d is an element of {7,..., 12} which satisfies the inequality l(2)(S) >= d - 3 + [d/2]. This shows that Noma's bound is no more valid for locally non- Cohen-Macaulay varieties.