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A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a smooth projective curve defined over an algebraically closed field k , and let F X denote the absolute Frobenius morphism of X when the characteristic of k is positive. A vector bundle over X is called virtually globally generated if its pull back, by some finite morphism to X from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of k is positive, a vector bundle E over X is virtually globally generated if and only if ( F X m ) * E E a E f for...

About G -bundles over elliptic curves

Yves Laszlo (1998)

Annales de l'institut Fourier

Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G ( X ) parametrizing S -equivalence classes of semistable G -bundles over an elliptic curve X is isomorphic to [ Γ ( T ) Z X ] / W . By a result of Looijenga, this shows that M G ( X ) is a weighted projective space.

Coherent sheaves with parabolic structure and construction of Hecke eigensheaves for some ramified local systems

Jochen Heinloth (2004)

Annales de l'Institut Fourier

The aim of these notes is to generalize Laumon’s construction [20] of automorphic sheaves corresponding to local systems on a smooth, projective curve C 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.

Montserrat Teixidor i Bigas (1998)

Collectanea Mathematica

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

Vincent Lafforgue, Sergey Lysenko (2011)

Bulletin de la Société Mathématique de France

We prove that the global geometric theta-lifting functor for the dual pair ( H , G ) is compatible with the Whittaker functors, where ( H , G ) is one of the pairs ( S 𝕆 2 n , 𝕊 p 2 n ) , ( 𝕊 p 2 n , S 𝕆 2 n + 2 ) or ( 𝔾 L n , 𝔾 L n + 1 ) . That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H .

Conformal blocks and cohomology in genus 0

Prakash Belkale, Swarnava Mukhopadhyay (2014)

Annales de l’institut Fourier

We give a characterization of conformal blocks in terms of the singular cohomology of suitable smooth projective varieties, in genus 0 for classical Lie algebras and G 2 .

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