On connected divisors.
On contractions of extremal rays of Fano manifolds.
On contributions of embedded components to intersection theory. II.
On contributions of embedded components to intersection theory, a first approach
On counterexamples to local-global divisibility in commutative algebraic groups
On covering and quasi-unsplit families of curves
Given a covering family of effective 1-cycles on a complex projective variety , we find conditions allowing one to construct a geometric quotient , with regular on the whole of , such that every fiber of is an equivalence class for the equivalence relation naturally defined by . Among other results, we show that on a normal and -factorial projective variety with canonical singularities and , every covering and quasi-unsplit family of rational curves generates a geometric extremal...
On covering systems on rings
On coverings of simple abelian varieties
To any finite covering of degree between smooth complex projective manifolds, one associates a vector bundle of rank on whose total space contains . It is known that is ample when is a projective space ([Lazarsfeld 1980]), a Grassmannian ([Manivel 1997]), or a Lagrangian Grassmannian ([Kim Maniel 1999]). We show an analogous result when is a simple abelian variety and does not factor through any nontrivial isogeny . This result is obtained by showing that is -regular in the...
On cubics and quartics through a canonical curve
We construct families of quartic and cubic hypersurfaces through a canonical curve, which are parametrized by an open subset in a grassmannian and a Flag variety respectively. Using G. Kempf’s cohomological obstruction theory, we show that these families cut out the canonical curve and that the quartics are birational (via a blowing-up of a linear subspace) to quadric bundles over the projective plane, whose Steinerian curve equals the canonical curve
On curves on rational normal scrolls.
On curves with a theta-characteristic whose space of sections has dimension 4.
On curves with natural cohomology and their deficiency modules
The minimal free resolution of the Hartshorne-Rao module of a curve with natural cohomology is studied, and conditions are given on the degrees and the ranks of the terms of this resolution.
On cycles and orbits of polynomial mappings
On Cycles in Flag Manifolds.
On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
On deformation method in invariant theory
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let be a reductive group, an affine -variety and a spherical subgroup. We show that whenever is affine and its semigroup of weights is saturated, the algebra of -invariant regular functions on has a -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of . The deformation method in its usual form, as developed...
On deformation of maximally degenerate stable marked curves and Oda's problem.
On Deformations and the Local Torelli Problem of Cyclic Branched Coverings.
On deformations of monomial curves
On Deformations of Quintic Surfaces.