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Vadim Schechtman

Publications and source records attributed to Vadim Schechtman.

At least 55 records · Page 3Linked to original sources
arXiv2014

Chiral De Rham complex over locally complete intersections

We define a version of a derived chiral De Rham complex over a locally complete intersection, thereby "chiralizing" a result by Illusie and Bhatt. A similar construction attaches to a graded ring a dg vertex algebra, which we prove to be Morita equivalent to a dg algebra of differential operators. For example, the dg vertex algebra associated to a fat point, which also arises in the Landau-Ginzburg model, is shown to be derived rational.

math.AG↗
arXiv2012

Remarks on a triple integral

We discuss real, p-adic and q-deformed versions of an integral related to Liouville field theory and triple $L$-functions.

math.QA↗
arXiv2012

Chiral differential operators on abelian varieties

The paper consists of two parts. In the first, we describe a way of getting from an algebra of chiral differential operators (cdo) on an abelian variety a cdo on the dual variety. The second is an introduction to the sigma-model on a torus and to the Wess-Zumino-Witten model from the cdo perspective.

math.AG↗
arXiv2011

Pentagramma Mirificum and elliptic functions

We give an exposition of fragments from Gauss [G] where he discovered, with the help of some work of Jacobi, a remarkable connection between Napier pentagons on the sphere and Poncelet pentagons on the plane. As a corollary we find a parametrization in elliptic functions of the classical dilogarithm five-term relation.

math.AG↗
arXiv2007

Nombres de Bernoulli et une formule de Ramanujan

In the first part we establish a connection between the Euler-Maclaurin summation formula and the Rota-Baxter functional equation. In the second part we give a simple proof of a formula, due to Ramanujan, on the summation of certain exponential series.

math.CA↗
arXiv2005

Algebres de Frobenius-Virasoro

In this note we associate to each Frobenius algebra a vertex algebra, the simplest example being the Virasoro vertex algebra. This construction is analogous to the procedure which associates to a Lie algebra with an invariant bilinear form the vacuum module over the corresponding Kac-Moody Lie algebra.

math.QA↗
arXiv2003

Sur les algèbres vertex attachées aux variétés algébriques

Sganarelle: ... Mais encore faut-il croire quelque chose dans le monde: qu'est-ce donc que vous croyez? Dom Juan: Ce que je crois? Sganarelle: Oui. Dom Juan: Je crois que deux et deux sont quatre, Sganarelle, et que quatre et quatre sont huit. [Molière, Dom Juan] One dicusses sheaves of vertex algebras over smooth varieties and their connections with characteristic classes.

math.AG↗
arXiv2000

Gerbes of chiral differential operators. III

This note is a sequel to "Gerbes of chiral differential operators. II", math.AG/0003170. We study gerbes of chiral differential operators acting on the exterior algebra $ΛE$ of a vector bundle over a smooth algebraic variety $X$. When $E=Ω^1_X$ this gerbe admits a canonical global section which coincides with the chiral de Rham complex of $X$.

math.AG↗
arXiv1999

Gerbes of chiral differential operators

In this note we compute the cohomological obstruction to the existence of certain sheaves of vertex algebras on smooth varieties. These sheaves have been introduced and studied in the previous work by A.Vaintrob and two of the authors. Hopefully our result clarifies to some extent the constructions of the above work.

math.AG↗
arXiv1999

Chiral de Rham complex

The aim of this note is to define certain sheaves of vertex algebras on smooth manifolds. For each smooth complex algebraic (or analytic) manifold $X$, we construct a sheaf $Ω^{ch}_X$, called the {\bf chiral de Rham complex} of $X$. It is a sheaf of vertex algebras in the Zarisky (or classical) topology, It comes equipped with a $\BZ$-grading by {\it fermionic charge}, and the {\it chiral de Rham differential} $d_{DR}^{ch}$, which is an endomorphism of degree 1 such that $(d_{DR}^{ch})^2=0$. One has a canonical embedding of the usual de Rham complex $(Ω_X, d_{DR})\hra (Ω_X^{ch}, d_{DR}^{ch})$ which is a quasiisomorphism. If $X$ is Calabi-Yau then this sheaf admits an N=2 supersymmetry. For some $X$ (for example, for curves or for the flag spaces $G/B$), one can construct also a purely even analogue of this sheaf, a {\it chiral structure sheaf} $\CO^{ch}_X$. For the projective line, the space of global sections of the last sheaf is the irreducible vacuum $\hsl(2)$-module on the critical level.

math.AG↗
arXiv1999

Chiral Poincaré duality

The aim of this note is to prove the analogue of Poincaré duality in the chiral Hodge cohomology.

math.AG↗