Related papers: Holomorphic symplectic geometry: a problem list

We discuss some examples of open manifolds which admit non-isomorphic symplectic structures of Liouville type.

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

This document collects contributions to the Open Problem List in Billiards and Quantitative Symplectic Geometry, compiled following discussions during the workshop ``Billiards and quantitative symplectic geometry'' that took place at the…

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…

This is a survey on algorithmic questions about combinatorial and geometric properties of convex polytopes. We give a list of 35 problems; for each the current state of knowledege on its theoretical complexity status is reported. The…

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.

The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for…

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…

We describe the space of Poisson bivectors near a log-symplectic structure up to small diffeomorphisms.

We present examples of prequantizations over integral symplectic manifolds which admit infinitely many smoothly trivial contact mapping classes. These classes are given by the connected components of the strict contactomorphism group which…

Some aspects of the multidimensional soliton geometry are considered.

Integrable Hamiltonian systems on symplectic manifolds have been well-studied. However, an intrinsic property of these kind of systems is that they can only live on even dimensional manifolds. To introduce a similar notion of integrability…

This text introduces geometric quantization on orbifolds. After reviewing the necessary background, it develops new treatments of prequantization, polarizations, and metaplectic correction for symplectic orbifolds.

This note is devoted to the study of the homology class of a compact Poisson transversal in a Poisson manifold. For specific classes of Poisson structures, such as unimodular Poisson structures and Poisson manifolds with closed leaves, we…

This is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this…

See math.CV/0509030 which replaces this paper.

We study symplectic structures on K\"ahler surfaces with p_g = 0. We give an example of a projective surface which admits a symplectic structure which is not compatible with any K\"ahler metric.

While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between…