Modulprobleme in der algebraischen Geometrie III
Motivic decomposition of abelian schemes and the Fourier transform.
Multiplicité et formes éliminantes
Non-obstructed subcanonical space curves.
Recall that a closed subscheme X ⊂ P is non-obstructed if the corresponding point x of the Hilbert scheme Hilbp(t)n is non-singular. A geometric characterization of non-obstructedness is not known even for smooth space curves. The goal of this work is to prove that subcanonical k-Buchsbaum, k ≤ 2, space curves are non-obstructed. As a main tool we use Serre's correspondence between subcanonical curves and vector bundles.
Non-obstructedness of Gorenstein Subschemes of Codimension 3 in P...
Normal Bundles of Rational Curves in ...3.
Note on curves in a jacobian
Numerical sections on elliptic surfaces
Obstructions to deforming curves on a -fold, II: Deformations of degenerate curves on a del Pezzo -fold
We study the Hilbert scheme of smooth connected curves on a smooth del Pezzo -fold . We prove that any degenerate curve , i.e. any curve contained in a smooth hyperplane section of , does not deform to a non-degenerate curve if the following two conditions are satisfied: (i) and (ii) for every line on such that , the normal bundle is trivial (i.e. ). As a consequence, we prove an analogue (for ) of a conjecture of J. O. Kleppe, which is concerned with non-reduced components...
On a cell decomposition of the Hilbert scheme of points in the plane.
On Chow rings of fine moduli spaces of modules.
On Equations Defining Arithmetically Cohen-Macaulay Schemes. I.
On geometry of binary symmetric models of phylogenetic trees
We investigate projective varieties which are binary symmetric models of trivalent phylogenetic trees. We prove that they have Gorenstein terminal singularities and are Fano varieties of index 4 and dimension equal to the number of edges of the tree in question. Moreover any two such varieties which are of the same dimension are deformation equivalent, that is, they are in the same connected component of the Hilbert scheme of the projective space. As an application we provide a simple formula for...
On Hodge structures and non-representability of Chow groups
On hypersurface quotient singularities of dimension 4.
On limiting rational curves.
On Linearly Normal Space Curves.
On Moduli of Algebraic Varieties. I.
On moduli of algebraic varieties II
On projective degenerations of Veronese spaces
Here we give several examples of projective degenerations of subvarieties of . The more important case considered here is the d-ple Veronese embedding of ; we will show how to degenerate it to the union of n-dimensional linear subspaces of and the union of scrolls. Other cases considered in this paper are essentially projective bundles over important varieties. The key tool for the degenerations is a general method due to Moishezon. We will give elsewhere several applications to postulation...