Vertex algebroids à la Beilinson-Drinfeld

Vertex Algebroids I

Vertex Algebroids Ii

In this note we determine the obstruction to triviality of the stack of exact vertex algebroids thereby recovering the result of [GMS]. The stack EVAOX of exact vertex OX-algebroids is a torsor under the stack in Picard groupoids ECAOX of exact Courant OX -algebroids. The latter is equivalent to the stack of torsors under ΩX −→Ω . Therefore, ECAOX -torsors are classified by H (X; ΩX −→Ω ). The ...

The Beilinson Equivalence for Differential Operators and Lie Algebroids

Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived cat...

Beilinson-Drinfeld chiral algebras for del Pezzo surfaces

Recently the chiral algebra of Beilinson-Drinfeld draws much attention in the mathematical physics of superstring theory. Naively, this is a holomorphic conformal field theory with integer graded conformal dimension, whose target space not necessarily has the vanishing first Chern class. This algebra has two ways of definition: one is that of Malikov-Schechtman-Vaintrob by gluing affine patches...

Quiver Varieties and Beilinson-drinfeld Grassmannians of Type A

We construct Nakajima’s quiver varieties of type A in terms of conjugacy classes of matrices and (non-Slodowy’s) transverse slices naturally arising from affine Grassmannians. In full generality quiver varieties are embedded into Beilinson-Drinfeld Grassmannians of type A. Our construction provides a compactification of Nakajima’s quiver varieties and a decomposition of an affine Grassmannian i...