A chracterization of A-discriminantal hypersurfaces in terms of the logarithmic Gauss map.
A counterexample to a conjecture on linear systems on .
A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
We compute the essential dimension of the functors Forms and Hypersurf of equivalence classes of homogeneous polynomials in variables and hypersurfaces in , respectively, over any base field of characteristic . Here two polynomials (or hypersurfaces) over are considered equivalent if they are related by a linear change of coordinates with coefficients in . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application of the...
A Geometrical approach to Gordan--Noether's and Franchetta's contributions to a question posed by Hesse.
A splitting criterion for rank 2 vector bundles on hypersurfaces in .
ACM bundles on general hypersurfaces in P5 of low degree.
In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P5 a rank 2 vector bundle ε splits if and only if h1ε(n) = h2ε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].
Ample line bundles on smooth surfaces.
An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
Calculating the Mordell-Weil rank of elliptic threefolds and the cohomology of singular hypersurfaces
In this paper we give a method for calculating the rank of a general elliptic curve over the field of rational functions in two variables. We reduce this problem to calculating the cohomology of a singular hypersurface in a weighted projective -space. We then give a method for calculating the cohomology of a certain class of singular hypersurfaces, extending work of Dimca for the isolated singularity case.
Change of polarization and Hodge numbers of moduli spaces of torsion free sheaves on surfaces.
Characterizing Moisezon Spaces by Almost Positive Coherent Analytic Sheaves.
Cobordism of algebraic knots via Seifert forms.
Construction d'hypersurfaces réelles
Curves on a ruled cubic surface.
For the general ruled cubic surface S (with a double line) in P3 = P3 sub k, k any algebraically closed field, we find necessary conditions for which curves on S can be the specialization of a flat family of curves on smooth cubics. In particular, no smooth curve of degree > 10 on S is such a specialization.
Détermination géométrique des sommes de Selberg-Evans
Divisors on hypersurfaces.
Durchmesser und Mittelpunkte algebraischer Hyperflächen.
Everywhere non reduced moduli spaces.
Families of hypersurfaces of large degree
Grauert and Manin showed that a non-isotrivial family of compact complex hyperbolic curves has finitely many sections. We consider a generic moving enough family of high enough degree hypersurfaces in a complex projective space. We show the existence of a strict closed subset of its total space that contains the image of all its sections.
Fano Schemes of Linear Spaces on Hypersurfaces.