Bases for the homology groups of the Hilbert scheme of points in the plane
Bases of homology spaces of the Hilbert scheme of points in an algebraic surface.
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.
Betti numbers for the Hilbert function strata of the punctual Hilbert scheme in two variables.
Birational Properties of Moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces.
Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.
Let X ⊂ P6 be a smooth irreducible projective threefold, and d its degree. In this paper we prove that there exists a constant β such that for all X containing a smooth ruled surface as hyperplane section and not contained in a fourfold of degree less than or equal to 15, d ≤ β. Under some more restrictive hypothesis we prove an analogous result for threefolds containing a smooth ruled surface as hyperplane section and contained in a fourfold of degree less than or equal to 15.