Second Chern class and Riemann-Roch for vector bundles on resolutions of surface singularities.
Sections du fibré déterminant sur l'espace de modules des faisceaux semi-stables de rang 2 sur le plan projectif
La conjecture de “dualité étrange” de Le Potier donne un isomorphisme entre l’espace des sections du fibré déterminant sur deux espaces de modules différents de faisceaux semi-stables sur le plan projectif . Si on considère deux classes orthogonales dans l’algèbre de Grothendieck telles que est de rang strictement positif et est de rang zéro, on note et les espaces de modules de faisceaux semi-stables de classe , respectivement , sur . Il existe sur (resp. ) un fibré déterminant...
Semistability of certain bundles on a quintic Calabi-Yau threefold.
Simple sheaves versus stable sheaves on algebraic surfaces.
Singularity of the moduli space of stable bundles on surfaces
Smooth Enriques surfaces in P4 and exceptional bundles.
Some nonreduced moduli of bundles and Donaldson invariants for Dolgachev surfaces.
Some polynomials on the blow-up of [...]
Some properties of stable rank 2 bundles on algebraic surfaces.
Special rank two vector bundles over Enriques surfaces.
Stability of tautological vector bundles on Hilbert squares of surfaces
Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.
In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit...
Stable bundles with torsion chern classes on non-Kählerian elliptic surfaces.
String theory and duality.
Symplectic structures on moduli spaces of framed sheaves on surfaces
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.
Syzygies and Koszul cohomology of smooth projective varieties for arbitrary dimension.