Related papers: Chiral de Rham complex

A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic…

In this paper we continue our work on Schwartz functions and generalized Schwartz functions on Nash (i.e. smooth semi-algebraic) manifolds. Our first goal is to prove analogs of de-Rham theorem for de-Rham complexes with coefficients in…

According to a statement by Pavel Etingof, in the special case of an affine variety $X$ with a faithful action by a finite group $G$, the sheaf of (twisted) Cherednik algebras $\mathcal{H}_{1, c, \psi, X, G}$ with formal parameters $c,…

We study the de Rham complex on a smooth manifold with a periodic end modeled on an infinite cyclic cover X' \to X. The completion of this complex in exponentially weighted L^2-norms is Fredholm for all but finitely many exceptional weights…

Introducing $h$- and $h'$-deformations of ${\mathbb Z}_2$-graded (1+2)- and (2+1)-spaces, denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$, a two-parameter first order differential calculus, de Rham complex, on ${\mathbb…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

For a smooth scheme $X$ over a perfect field $k$ of positive characteristic, we define (for each $m\in\mathbb{Z}$) a sheaf of rings $\mathcal{\widehat{D}}_{W(X)}^{(m)}$ of differential operators (of level $m$) over the Witt vectors of $X$.…

We construct a geometric version of BRST cohomology complex of a chiral module over a Lie-* algebra using the language of differential graded Lie algebroids in the category of D-modules on a compact curve $X$.

Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…

Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…

For a reduced pure dimensional complex space $X$, we show that if Barlet's recently introduced sheaf $\alpha_X^1$ of holomorphic $1$-forms or the sheaf of germs of weakly holomorphic $1$-forms is locally free, then $X$ is smooth. Moreover,…

We construct representations of the deformed Shatashvili-Vafa vertex algebra $\mathrm{SV}_a$, with parameter $a \in \mathbb{C}$, as recently proposed in the physics literature by Fiset and Gaberdiel. The geometric input for our construction…

In this paper we study the vertex operator algebra $\mathscr D^{\text{ch}}(\mathbb H,\Gamma)$ constructed from the fixed points of the chiral differential operators on the upper half plane which is holomorphic at all the cusps, under the…

Let $X$ be a complex analytic manifold, $D\subset X$ a free divisor with jacobian ideal of linear type (e.g. a locally quasi-homogeneous free divisor), $j: U=X-D \to X$ the corresponding open inclusion, $E$ an integrable logarithmic…

We review different constructions of the supersymmetry subalgebras of the chiral de Rham complex on special holonomy manifolds. We describe the difference between the holomorphic-anti-holomorphic sectors based on a local free ghost system…

The graded coherent sheaf $\alpha_X^\bullet$ constructed in [B.18] for any reduced pure dimensional complex space $X$ is stable by exterior product but not by the de Rham differential. We construct here a new graded coherent sheaf…

In this paper, we give a unified construction of vertex algebras arising from infinite-dimensional Lie algebras, including the affine Kac-Moody algebras, Virasoro algebras, Heisenberg algebras and their higher rank analogs, orbifolds and…

We introduce a new variant of Hochschild's two-sided bar construction for the setting of curved differential graded algebras. One can geometrically think of the classical bar complex as elements from the algebra positioned along different…

Let $({\bf X},\omega_{\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf X}=n\in\mathbb…

To a smooth and proper morphism $\mathcal{X}\to U$ with quasicompact semiseparated target we associate a sheaf in the \'etale topology, which takes an affine $U$-scheme $V$ to the set of $V$-linear semiorthogonal decompositions (of fixed…