A description of Chern classes of semistable sheaves on a quadric surface.
A footnote to a paper by Noma
Let be a globally generated ample vector bundle of rank on a complex projective smooth surface . By extending a recent result by A. Noma, we classify pairs as above satisfying .
A Foruier-Mukai transform for stable bundles on K3 surfaces.
A note about the isotropy groups of 2-plane bundles over closed surfaces.
A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4
We prove that a certain Brill-Noether locus over a non-hyperelliptic curve C of genus 4, is isomorphic to the Donagi-Izadi cubic threefold in the case when the pencils of the two trigonal line bundles of C coincide.
A Note on compact Kähler manifolds with Nef Tangent Bundles.
À propos de la construction de l'espace de modules des faisceaux semi-stables sur le plan projectif
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].
Algebraic complete integrability of an integrable system of Beauville
We show that the Beauville’s integrable system on a ten dimensional moduli space of sheaves on a K3 surface constructed via a moduli space of stable sheaves on cubic threefolds is algebraically completely integrable, using O’Grady’s construction of a symplectic resolution of the moduli space of sheaves on a K3.
Ample line bundles on blown up surfaces.
Ample vector bundles with sections vanishing along conic fibrations over curves.
Ample vector bundles with zero loci having a bielliptic curve section.
Applications of the Ein-Lazarsfeld cirterion for spannedness of adjoint bundles.
Atiyah Classes and Closed Forms on Moduli Spaces of Sheaves
Bilinear forms and extremal Kähler vector fields associated with Kähler classes.
Birational Properties of Moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces.
Bogomolov instability of higher rank sheaves on surfaces in characteristic p.
Bounds for stable bundles and degrees of Weierstrass schemes.
Bubble tree compactification of moduli spaces of vector bundles on surfaces
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c 1 = 0, c 1...