Seminars

Title: Borel covering for Hilbert schemes.

Abstract:

Let J be a Borel (strongly stable) monomial ideal in a polynomial ring P over a field k. We will show that there is an affine variety BSt(J) parametrizing  all the ideals I in P such that the set of monomials not contained in J is a basis for the quotient P/I as k-vector space. As an application we will see that every Hilbert scheme of subvarieties of the projective space Pn has an open covering given by affine varieties of the type BSt(J) and obtain properties of their defining  equations  in the Plucker coordinates.