Bounds on multisecant lines

Abstract

The purpose of this paper is twofold.First, we give an upper bound on the order of a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in P n of codimension two in terms of the Hilbert function.Secondly, we give an explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal.This description is used to refine a standard linking theorem.These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems.