Betti numbers for the Hilbert function strata of the punctual Hilbert scheme in two variables.
Birational invariants in the case of prime characteristic.
Borel ideals in three variables.
Bounds for Castelnuovo's regularity and the genus of projective varieties
Bounds on multisecant lines.
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 Pn 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,...