Related papers: Sheaves on P^1 x P^1, bigraded resolutions, and co…

We show that the Poisson structure on the smooth locus of a moduli space of 1-dimensional sheaves on a Poisson projective surface $X$ over $\mathbb C$ is a reduction of a natural symplectic structure.

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M_H(S,P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure…

Since a Poisson Structure is a smooth bivector field, we use a ring-valued sheaf $\OO_{X}$ on a manifold with corners $X$, we can interpret $\OO_{X}(U)$ as the ring of admissible smooth functions where $U$ is an open subset on $X$, in this…

We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases…

We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…

Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…

We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general…

We study sheaves on holomorphic spaces of loops and apply this to the study of the complex, defined in \cite{BdSHK}, governing deformations of the \emph{Poisson vertex algebra} structure on the space of holomorphic loops into a Poisson…

We combine the projective geometry approach to Schroedinger equations on the circle and differential Galois theory with the theory of Poisson Lie groups to construct a natural Poisson structure on the space of wave functions (at the zero…

We study the supergeometry of complex projective superspaces $\mathbb{P}^{n|m}$. First, we provide formulas for the cohomology of invertible sheaves of the form $\mathcal{O}_{\mathbb{P}^{n|m}} (\ell)$, that are pull-back of ordinary…

In this paper, we study the invariant theory of quadratic Poisson algebras. Let G be a finite group of the graded Poisson automorphisms of a quadratic Poisson algebra A. When the Poisson bracket of A is skew-symmetric, a Poisson version of…

We present a class of Poisson structures on trivial extension algebras which generalize some known structures induced by Poisson modules. We show that there exists a one-to-one correspondence between such a class of Poisson structures and…

We classify all of the 4-dimensional linear Poisson structures of which the corresponding Lie algebras can be considered as the extension by a derivation of 3-dimensional unimodular Lie algebras. The affine Poisson structures on R^3 are…

We produce natural quadratic Poisson structures on moduli spaces of representations of quivers. In particular, we study a natural Poisson structure for the generalised Kronecker quiver with 3 arrows.

We study the moduli of G-local systems on smooth but not necessarily proper complex algebraic varieties. We show that, when suitably considered as derived algebraic stacks, they carry natural Poisson structures, generalizing the well known…

This paper is devoted to the study of Poisson structures on the Euclidean four dimensional space R4. By using the properties of the trace operator associated to a volumen form and the elementary vector calculus operations in R3, we give…

Let $P$ be a Poisson structure on a finite-dimensional affine real manifold. Can $P$ be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach -- with respect to all affine Poisson…

In this paper, we study deformations of nonsingular Poisson varieties, deformations of Poisson invertible sheaves and simultaneous deformations of nonsingular Poisson varieties and Poisson invertible sheaves, which extend flat deformation…

We give classifications of linear orbits of pairs of square matrices with non-vanishing discriminant polynomials over a field in terms of certain coherent sheaves with additional data on closed subschemes of the projective line. Our results…