Related papers: Poisson deformations and birational geometry
Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance,…
Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…
Let X be a an affine smooth symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and A be its deformation quantization over the p-adic integers. We prove that for all $n\geq 1,$ the Hochschild cohomogy of $A/p^nA$ is isomorphic to the de…
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form…
The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…
The unimodularity condition for a Poisson structure (ie., a Poisson structure with a trivial modular class) induces a Poincar\'e duality between its Poisson homology and its Poisson cohomology. Therefore an information about the Poisson…
It is shown that coassociative cones in R^7 that are r-oriented and ruled by 2-planes are equivalent to CR-holomorphic curves in the oriented Grassmanian of 2-planes in R^7. The geometry of these CR-holomorphic curves is studied and related…
We study the birational geometry of deformations of Hilbert schemes of points on the projective plane P2. We complete the picture in the paper of Daniele Arcara, Aaron Bertram, Izzet Coskun and Jack Huizenga by giving an explicit…
Consider a finite collection of affine hyperplanes in $\mathbb R^d$. The hyperplanes dissect $\mathbb R^d$ into finitely many polyhedral chambers. For a point $x\in \mathbb R^d$ and a chamber $P$ the metric projection of $x$ onto $P$ is the…
Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence…
Let $O$ be a nilpotent orbit of a complex semisimple Lie algebra $\mathfrak{g}$ and let $\pi: X \to \bar{O}$ be the finite covering associated with the universal covering of $O$. In the previous article we have explicitly constructed a…
Whenever a given Poisson manifold is equipped with discrete symmetries the corresponding algebra of invariant functions or the algebra of functions twisted by the symmetry group can have new deformations, which are not captured by…
The Hopf dual $H^\circ$ of any Poisson Hopf algebra $H$ is proved to be a co-Poisson Hopf algebra provided $H$ is noetherian. Without noetherian assumption, it is not true in general. There is no nontrivial Poisson Hopf structure on the…
Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order…
This is the first of two papers, in which we prove a version of Conn's linearization theorem for the Lie algebra $\mathfrak{sl}_2(\mathbb{C})\simeq \mathfrak{so}(3,1)$. Namely, we show that any Poisson structure whose linear approximation…
We study a deformation of a $2$-graded Poisson algebra where the functions of the phase space variables are complemented by linear functions of parity odd velocities. The deformation is carried by a $2$-form $B$-field and a bivector $\Pi$,…
We construct a class of quantum field theories depending on the data of a holomorphic Poisson structure on a piece of the underlying spacetime. The main technical tool relies on a characterization of deformations and anomalies of such…
Motivated by physics, we propose two conjectures regarding the cohomology ring of the crepant resolutions of orbifolds and cohomological invariants of K-equivalent manifolds.
The correspondence between Poisson structures and symplectic groupoids, analogous to the one of Lie algebras and Lie groups, plays an important role in Poisson geometry; it offers, in particular, a unifying framework for the study of…
We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of…