A Foruier-Mukai transform for stable bundles on K3 surfaces.
A Hirzebruch-Riemann-Roch formula for analytic spaces and non-projective algebraic varieties
A home-made Hartshorne-Serre correspondence.
A Noether-Lefschetz theorem for vector bundles.
A note on certain Tannakian group schemes
In this note, we prove that the -fundamental group scheme is a birational invariant for smooth projective varieties. We prove that the -fundamental group scheme is naturally a quotient of the Nori fundamental group scheme. For elliptic curves, it turns out that the -fundamental group scheme and the Nori fundamental group scheme coincide. We also consider an extension of the Nori fundamental group scheme in positive characteristic using semi-essentially finite vector bundles, and prove that in...
A Note on compact Kähler manifolds with Nef Tangent Bundles.
A priori bounds of Castelnuovo type for cohomological Hilbert functions.
A propos de l' espace des modules de fibrés de rang 2 sur une courbe.
À propos de la construction de l'espace de modules des faisceaux semi-stables sur le plan projectif
À propos de l'existence de fibrés stables sur les surfaces.
A remark on the Chern class of a tensor product.
A Riemann-Roch theorem for flat bundles, with values in the algebraic Chern-Simons theory.
A Sharp Bound for the Number of Points where a Rank 3 Stable Reflexive Sheaf is not Free.
A splitting criterion for rank 2 vector bundles on hypersurfaces in .
A theorem on the adjoint system for vector bundles.
A Vanishing Theorem for Group Compactifications.
About -bundles over elliptic curves
Let be a complex algebraic group, simple and simply connected, a maximal torus and the Weyl group. One shows that the coarse moduli space parametrizing -equivalence classes of semistable -bundles over an elliptic curve is isomorphic to . By a result of Looijenga, this shows that is a weighted projective space.
About restricting 2-bundles on IP3 to planes.
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].
ACM bundles, quintic threefolds and counting problems
We review some facts about rank two arithmetically Cohen-Macaulay bundles on quintic threefolds. In particular, we separate them into seventeen natural classes, only fourteen of which can appear on a general quintic. We discuss some enumerative problems arising from these.