Related papers: Deformations of holomorphic Poisson manifolds

We shall prove that the Poisson deformation functor of an affine (singular) symplectic variety is unobstructed. As a corollary, we prove the following result. Theorem: For an affine symplectic variety $X$ with a good $C^*$-action (where its…

We prove that for every smooth prime Fano $3$-fold $V$, the Hilbert scheme $\operatorname{Hilb}^{sc} V$ of smooth connected curves on $V$ contains a generically non-reduced irreducible component of Mumford type. We also study the…

We consider surfaces immersed in three-dimensional pseudohermitian manifolds. We define the notion of (p-)mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group.…

We prove that if a compact K\"ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite \'etale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson…

In this paper, we define a concept of a family of compact holomorphic Poisson manifolds on the basis of Kodaira-Spencer's deformation theory and deduce the integrability condition. We prove an analogue of their `Theorem of existence for…

A classical result in complex geometry says that the automorphism group of a manifold of general type is discrete. It is more generally true that there are only finitely many surjective morphisms between two fixed projective manifolds of…

In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…

We give a characterisation of Atiyah's and Hitchin's transverse Hilbert schemes of points on a symplectic surface in terms of bi-Poisson structures. Furthermore, we describe the geometry of hyperk\"ahler manifolds arising from the…

We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson algebraic structure on the space of smooth functions of the…

We prove a compactness theorem for holomorphic curves in 4-dimensional symplectizations that have embedded projections to the underlying 3-manifold. It strengthens the cylindrical case of the SFT compactness theorem by using intersection…

Deformation theory is treated for locally notherian formal schemes (non necessarily smooth). The cotangent complex is defined in the derived category through the homology localization functor. The basic properties and results of a…

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…

Given a smooth compact complex surface together with a holomorphic line bundle on it, using the theory of Hodge modules, we compute the twisted Hodge groups/numbers of Hilbert schemes (or Douady spaces) of points on the surface with values…

The present paper provides several results on automorphisms of hyperk\"ahler (or irreducible holomorphic symplectic) manifolds. In particular it focuses on the symplectic case and contains a classification of prime order symplectic…

In this paper, generalizing the techniques of Bour's theorem, we prove that every generic cuspidal edge, more generally, generic $n$-type edge, which is invariant under a helicoidal motion in Euclidean $3$-space admits non-trivial isometric…

The Serre construction of rank two holomorphic bundles with a section is adapted to construct generalized holomorphic bundles on a generalized complex 4-manifold from the data of a set of points on an elliptic curve. The motivation is the…

Rational curves on Hilbert schemes of points on $K3$ surfaces and generalised Kummer manifolds are constructed by using Brill-Noether theory on nodal curves on the underlying surface. It turns out that all wall divisors can be obtained, up…

We study neighbourhoods of submanifolds in generalized complex geometry. Our first main result provides sufficient criteria for such a submanifold to admit a neighbourhood on which the generalized complex structure is B-field equivalent to…

We study symplectic forms on hypersurface algebroids. These are a broad generalization of the $b^{k}$-Poisson structures studied extensively by Miranda, Scott, and collaborators, and their geometry is intimately related to the group of…

We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp.…