Related papers: Symplectic Birational Geometry
In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.
In this paper we analyse the birational geometry of O'Grady ten dimensional manifolds, giving a characterisation of Kaehler classes and lagrangian fibrations. Moreover, we study symplectic compactifications of intermediate jacobian…
In this paper we study the birational geometry of HyperKaehler manifolds by combining the method of minimal model program and the traditional approach of symplectic geometry.
A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and…
This article contains the notes of a graduate course on birational geometry focusing on the minimal model program. Topics covered include singularities, vanishing, nonvanishing, cone and contraction, base point freeness, finite generation,…
We prove the conjecture that two projective symplectic resolutions for a symplectic variety $W$ are related by Mukai's elementary transformations over $W$ in codimension 2 in the following cases: (i). nilpotent orbit closures in a classical…
The mathematical theory underlying Hamiltonian mechanics is called symplectic geometry. So symplectic geometry arose from the roots of mechanics and is seen as one of the most valuable links between physics and mathematics today. Symplectic…
This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].
In this paper we introduce the notion of relative Kodaira dimension for a symplectic 4-manifold M with a possibly disconnected embedded symplectic surface F. One notable feature is that the sphere components of F have to be discarded, which…
In this note, the geography problem in dimension four is reviewed and then its extension to dimension six for the symplectic case is explained. Finally some examples in dimension six are provided.
We discuss symplectic structures for the chiral boson in (1+1) dimensions and the self-dual field in (4k+2) dimensions. Dimensional reduction of the six-dimensional field on a torus is also considered.
This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
In this note we discuss the effect of the symplectic sum along spheres in symplectic four-manifolds on the Kodaira dimension of the underlying symplectic manifold. We find that the Kodaira dimension is non-decreasing. Moreover, we are able…
It is shown that the notion of W_\infty-algebra originally carried out over a (compact) Riemann surface can be extended to n complex dimensional (compact) manifolds within a symplectic geometrical setup. The relationships with the…
Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…
In this paper we analyze in detail a collection of motivating examples to consider $b^m$-symplectic forms and folded-type symplectic structures. In particular, we provide models in Celestial Mechanics for every $b^m$-symplectic structure.…
The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…
These lectures give a short introduction to the study of curves on algebraic varieties. After an elementary proof of the dimension formula for the space of curves, we summarize the basic properties of uniruled and of rationally connected…
For oriented surfaces $\Sigma$ with boundary, we consider the infinite-dimensional deformation space of projective structures on $\Sigma$ with nondegenerate boundary, up to isotopies fixing the boundary. We show that this space carries a…