Holomorphic vector bundles on
Homological projective duality
We introduce a notion of homological projective duality for smooth algebraic varieties in dual projective spaces, a homological extension of the classical projective duality. If algebraic varieties X and Y in dual projective spaces are homologically projectively dual, then we prove that the orthogonal linear sections of X and Y admit semiorthogonal decompositions with an equivalent nontrivial component. In particular, it follows that triangulated categories of singularities of these sections are...
Homotopiegruppen des Modulraumes MIP2 (?l,c2).
Homotopy properties of algebraic vector bundles.
Indecomposable Quadratic Bundles of rank 4n over the Real Affine Plane.
Instanton bundles on Fano threefolds
We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.
Instanton sheaves on complex projective spaces.
We study a class of torsion-free sheaves on complex projective spaces which generalize the much studied mathematical instanton bundles. Instanton sheaves can be obtained as cohomologies of linear monads and are shown to be semistable if its rank is not too large, while semistable torsion-free sheaves satisfying certain cohomological conditions are instanton. We also study a few examples of moduli spaces of instanton sheaves.
Intersection Homology II.
Intersection pairings in moduli spaces of holomorphic bundles on a Riemann surface.
Invariants symétriques et fibrés vectoriels sur les courbes.
Invertible ideals in real holomorphy rings.
Irreducibility of the Space of Mathematical Instanton Bundles with Rank 2 and c2 = 4.
Jacobians and differents of projective varieties.
Kodaira Dimension of Algebraic Fiber Spaces Over Curves.
Kodaira dimensíon of moduli space of vector bundles on surfaces.
Komplexe Unterräume und holomorphe Vektorraumbündel vom Rang zwei.
Komplexní vesmír Rogera Penrose
Koszul duality and semisimplicity of Frobenius
A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of -adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated...
La correspondance de Langlands sur les corps de fonctions
La méthode d'Horace pour l'interpolation à plusieurs variables.