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An example of an asymptotically Chow unstable manifold with constant scalar curvature

Hajime Ono, Yuji Sano, Naoto Yotsutani (2012)

Annales de l’institut Fourier

Donaldson proved that if a polarized manifold ( V , L ) has constant scalar curvature Kähler metrics in c 1 ( L ) and its automorphism group Aut ( V , L ) is discrete, ( V , L ) is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where Aut ( V , L ) is not discrete.

Bases of homology spaces of the Hilbert scheme of points in an algebraic surface.

C. Hermoso, I. Sols (1996)

Revista Matemática de la Universidad Complutense de Madrid

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.

Boundedness for threefolds in P6 containing a smooth ruled surface as hyperplane section.

Pietro Sabatino (2005)

Revista Matemática Complutense

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.

Codimension 3 Arithmetically Gorenstein Subschemes of projective N -space

Robin Hartshorne, Irene Sabadini, Enrico Schlesinger (2008)

Annales de l’institut Fourier

We study the lowest dimensional open case of the question whether every arithmetically Cohen–Macaulay subscheme of N is glicci, that is, whether every zero-scheme in 3 is glicci. We show that a general set of n 56 points in 3 admits no strictly descending Gorenstein liaison or biliaison. In order to prove this theorem, we establish a number of important results about arithmetically Gorenstein zero-schemes in 3 .

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