Reduced Hilbert schemes for irreducible curve singularities (Q1184027)

Let \(k\) be a field and let \(A\) be a local integral noetherian \(k\)-algebra of dimension one such that its normalization \(\bar A\) is a discrete valuation ring with residue field \(k\). The authors study the Hilbert scheme of zero-dimensional subschemes of Spec\((A)\). They prove that its connected components \({\mathcal M}_ \tau\) parametrize the ideals of \(A\) of colength \(\tau\). Furthermore \({\mathcal M}_ \tau\) are embedded in a linear subspace \({\mathcal M}\) of a certain Grassmannian. The authors study the partition of \({\mathcal M}\) by its intersection with the Schubert cells. They end the paper investigating the structure of \({\mathcal M}\) in the case of rings \(A\) with monomial semigroups.