We find two basis of the spaces of rational homology of the Hilbert scheme of points in an algebraic surface, by exhibiting two candidates having as cardinalities the known Betti numbers of this scheme and showing that both intersect in a matrix of nonzero determinant.
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,...