Related papers: Integration of the elliptic tangent bundle and ell…

The first part of this paper is a generalization of the Feix-Kaledin theorem on the existence of a hyperkahler metric on a neighbourhood of the zero section of the cotangent bundle of a Kahler manifold. We show that the problem of…

We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…

We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integration as a symplectic quotient, in the spirit of the Poisson…

Using Fedosov's approach we give a geometric construction of a formal symplectic groupoid over any Poisson manifold endowed with a torsion-free Poisson contravariant connection. In the case of Kaehler-Poisson manifolds this construction…

For a smooth complex algebraic curve $X$ and a reduced effective divisor $D$ on $X$, we introduce a notion of $D$-level structure on parahoric $\mathcal{G}_{\boldsymbol \theta}$-torsors over $X$, for any connected complex reductive Lie…

We consider a class of complex manifolds constructed as multiplicative quiver varieties associated with a cyclic quiver extended by an arbitrary number of arrows starting at a new vertex. Such varieties admit a Poisson structure, which is…

In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation. It is also proved that if a Lie group acts…

By considering suitable Poisson groupoids, we develop an approach to obtain Lie group structures on (subgroups of) the Poisson diffeomorphism groups of various classes of Poisson manifolds. As applications, we show that the Poisson…

In this paper we study the moduli stack of complexes of vector bundles (with chain isomorphisms) over a smooth projective variety $X$ via derived algebraic geometry. We prove that if $X$ is a Calabi-Yau variety of dimension $d$ then this…

Coupling Dirac structures are Dirac structures defined on the total space of a fibration, generalizing hamiltonian fibrations from symplectic geometry, where one replaces the symplectic structure on the fibers by a Poisson structure. We…

In this paper we study quotients of Lie algebroids and groupoids endowed with compatible differential forms. We identify Lie theoretic conditions under which such forms become basic and characterize the induced forms on the quotients. We…

We demonstrate the construction of Poisson structures via Lie algebroids on moduli spaces of twisted stable Higgs bundles over stacky curves. The construction provides new examples of Poisson structures on such moduli spaces. Special…

We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,\pi)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures…

We extend some fundamental definitions and constructions in the established generalisation of Lie theory involving Lie groupoids by reformulating them in terms of groupoids internal to a well-adapted model of synthetic differential…

We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson-Lie group $GL_n$ and derive from it a generalized cluster structure on $GL_n$ compatible with the push-forward…

The general theory of boundary value problems for linear elliptic wedge operators (on smooth manifolds with boundary) leads naturally, even in the scalar case, to the need to consider vector bundles over the boundary together with general…

We prove that the cotangent of a double Lie groupoid S has itself a double groupoid structure with sides the duals of associated Lie algebroids, and double base the dual of the Lie algebroid of the core of S. Using this, we prove a result…

We introduce a functional realization of the Hamiltonian structure on the moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup in SL_n. We also introduce a construction of the corresponding quantum algebras.

A vertical exterior derivative is constructed that is needed for a graded Poisson structure on multisymplectic manifolds over nontrivial vector bundles. In addition, the properties of the Poisson bracket are proved and first examples are…

We give a wide class of Lie-Poisson systems for which explicit, Lie-Poisson integrators, preserving all Casimirs, can be constructed. The integrators are extremely simple. Examples are the rigid body, a moment truncation, and a new, fast…