Related papers: Normal differential operators and deformation theo…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We classify subalgebras of a ring of differential operators which are big in the sense that the extension of associated graded rings is finite. We show that these subalgebras correspond, up to automorphisms, to uniformly ramified finite…

The first part of this paper provides a new formulation of chiral differential operators (CDOs) in terms of global geometric quantities. The main result is a recipe to define all sheaves of CDOs on a smooth cs-manifold; its ingredients…

Normal forms allow the use of a restricted class of coordinate transformations (typically homogeneous polynomials) to put the bifurcations found in nonlinear dynamical systems into a few standard forms. We investigate here the consequences…

We first want to consider the formal deformation of a fibered manifold $P \rightarrow M$ as a (bi-)module or subalgebra, where $M$ has a given differential star product. Consequently we want to find obstructions for the existence of a…

We establish a linear variational principle extending the Deville-Godefroy-Zizler's one. We use this variational principle to prove that if $X$ is a Banach space having property $(\alpha)$ of Schachermayer and $Y$ is any banach space, then…

Let X be a standard determinantal scheme X \subset \PP^n of codimension c, i.e. a scheme defined by the maximal minors of a t \times (t+c-1) homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf…

This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally $\mathcal{O}$-operators on Lie algebras, by means of the differential graded Lie algebra approach.…

A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…

A transforation between a hierarchy of integrable equations arising from the standard $R$-matrix construction on the algebra of differential operators and a hierarchy of integrable equations arising from a deformation of the standard…

It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…

The notion of pseudo-differential operators with coefficients in a continuous trace algebra over a manifold are introduced and their index theory is studied. The algebra of principal symbols in this calculus provides an abstract Poincar\'e…

We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…

The universal Spencer and de Rham complexes of sheaves over a smooth or analytical manifold are well known to play a basic role in the theory of $\mathcal{D}$-modules. In this article we consider a double complex of sheaves generalizing…

We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of…

It is a classic result that the geometry of the total space of a principal bundle with reference to the action of the bundle's structure group is codified in the bundle's operation, a collection of derivations comprising the de Rham…

We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a…

We generalize the Generic Model Theorem for equivariant presheaves of structures; extending the results of Macintyre and Caicedo. We also introduce a new class of generic cohomologies and show how, for some examples, they simplify to non…

Let F be a smooth real manifold with a linear connection in the tangent bundle. How can we extend the coefficients of the connection to bi-differential operators that incorporate the original structure at zero order? Take a constant mapping…