A Castelnuovo bound for smooth surfaces.
A proof of Noether's formula for the arithmetic genus of an algebraic surface
A Remark on K1 of an Algebraic Surface.
Algebraic equivalence modulo rational equivalence on a cubic threefold
Algebraic Fermi curves
An improved bound for the degree of smooth surfaces in not of general type
Are rational curves determined by tangent vectors?
Let be a projective variety which is covered by rational curves, for instance a Fano manifold over the complex numbers. In this paper, we give sufficient conditions which guarantee that every tangent vector at a general point of is contained in at most one rational curve of minimal degree. As an immediate application, we obtain irreducibility criteria for the space of minimal rational curves.
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.
Birational Morphisms Factorizable by two Monoidal Transformations.
Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface
Cohomological Dimension of Non-Complete Hypersurfaces.
Convex bodies associated to linear series
In his work on log-concavity of multiplicities, Okounkov showed in passing that one could associate a convex body to a linear series on a projective variety, and then use convex geometry to study such linear systems. Although Okounkov was essentially working in the classical setting of ample line bundles, it turns out that the construction goes through for an arbitrary big divisor. Moreover, this viewpoint renders transparent many basic facts about asymptotic invariants of linear series, and opens...
Curves on generic hypersurfaces
Curves on surfaces of degree 2r-... in Pr.
Deformations of cones over hyperelliptic curves.
Die Homologiegruppen singularitätenfreier algebraischer Hyperflächen
Die Sätze von Bertini für lokale Ringe.
Duality in the flat cohomology of a surface
Erratum: “Curves on generic hypersurfaces”
Examples of liftings of surfaces and a problem in de Rham cohomology