Related papers: A classification of star log symplectic structures…

Let \pi: Y -> X be a crepant projective resolution of an affine symplectic variety X with a good C^*-action. We interpret the second cohomology H^2(Y, C) in two ways. First, H^2(Y, C) is the Picard group of Y tensorised with C. By the ample…

The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in…

We make cohomological computations related to the moduli space of genus three curves with symplectic level two structure by means of counting points over finite fields. In particular, we determine the cohomology groups of the quartic locus…

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.

We give a classification of compact solitons for the pluriclosed flow on complex surfaces. First, by exploiting results from the Kodaira classification of surfaces, we show that the complex surface underlying a soliton must be K\"ahler…

Let $M$ be a smooth closed orientable manifold and $\mathcal{P}(M)$ the space of Poisson structures on $M$. We construct a Poisson bracket on $\mathcal{P}(M)$ depending on a choice of volume form. The Hamiltonian flow of the bracket acts on…

Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a…

The complex projective structures considered is this article are compact curves locally modeled on $\mathbb{CP}^1$. To such a geometric object, modulo marked isomorphism, the monodromy map associates an algebraic one: a representation of…

We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical $r$-matrices and matched pairs induced by Poisson…

We study the behavior of the modular class of an orientable Poisson manifold and formulate some unimodularity criteria in the semilocal context, around a (singular) symplectic leaf. Our results generalize some known unimodularity criteria…

The main purpose of the paper is to study hyperkahler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkahler structures. Motivated by the work of…

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

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.

This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…

Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the…

Given a smooth curve on a smooth surface, the Hilbert scheme of the surface is stratified according to the length of the intersection with the curve. The strata are highly singular. We show that this stratification admits a natural…

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 prove Lefschetz type theorems for cohomology groups and Picard groups of degeneracy loci for vector bundle maps. We also treat the case of antisymmetric maps.

Cohomology support loci of rank one local systems of a smooth quasiprojective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group. Tangent spaces of the…

On a manifold equipped with a bivector field, we introduce for every Hamiltonian a Lagrangian on paths valued in the cotangent space whose stationary points projects onto Hamiltonian vector fields. We show that the remaining components of…