A characterization of ample vector bundles on a curve.
A Class of Indecomposable Algebraic Vector Bundles.
A criterion for the existence of a flat connection on a parabolic vector bundle.
A criterion for virtual global generation
Let be a smooth projective curve defined over an algebraically closed field , and let denote the absolute Frobenius morphism of when the characteristic of is positive. A vector bundle over is called virtually globally generated if its pull back, by some finite morphism to from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of is positive, a vector bundle over is virtually globally generated if and only if for...
A duality result for moduli spaces of semistable sheaves supported on projective curves
A modular compactification of the general linear group.
A Narasimhan-Seshardri-Donaldson Correspondance over Non-orientable 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 remark on Hodge cycles on moduli spaces of rank 2 bundles over curves.
A sharp slope inequality for general stable fibrations of curves.
Abelian varieties in and points of bounded degree on algebraic curves
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.
Ample vector bundles with sections vanishing along conic fibrations over curves.
Auslander-Reiten components for concealed-canonical algebras
Brill-Noether theory for non-special linear systems
Canonical generators of the cohomology of moduli of parabolic bundles on curves.
Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems
The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve to the case of local systems with indecomposable unipotent ramification at a finite set of points. To this end we need an extension of the notion of parabolic structure on vector bundles to coherent sheaves. Once we have defined this, a lot of arguments from the article “ On the geometric Langlands conjecture” by Frenkel, Gaitsgory and Vilonen [11]...
Compactifications of moduli spaces of (semi)stable bundles on singular curves: two points of view.
Moduli spaces of vector bundles on families of non-singular curves are usually compactified by considering (slope)semistable bundles on stable curves. Alternatively, one could consider Hilbert-stable curves in Grassmannians. We study some properties of the latter and compare them with similar properties of curves coming from the former compactification. This leads to a new interpretation of the moduli space of (semi)stable torsion-free sheaves on a fixed nodal curve. One can present it as a quotient...
Compatibility of the theta correspondence with the Whittaker functors
We prove that the global geometric theta-lifting functor for the dual pair is compatible with the Whittaker functors, where is one of the pairs , or . That is, the composition of the theta-lifting functor from to with the Whittaker functor for is isomorphic to the Whittaker functor for .
Conformal blocks and cohomology in genus 0
We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus for classical Lie algebras and .