Resumen de Bounds on multisecant lines

Scott Nollet

• 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 $\mathbb{P}^n$ 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.