Related papers: Symplectic singularities

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In…

Let $\Omega$ be a non-singular syplectic form on some vector space $V$. Denote by $S^{n}_{k}(\Omega)$ the set of all $k$-dimensional planes $s$ in $V$ such that the restriction of $\Omega$ onto $s$ is singular. For the cases when $k=2,n-2$…

We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precisely, for each inertial class in the…

Let $(X, \omega)$ be a conical symplectic variety of dimension $2n$ which has a projective symplectic resolution. Assume that $X$ admits an effective Hamiltonian action of an $n$-dimensional algebraic torus $T^n$, compatible with the…

In this paper, we shall prove that any two (projective) symplectic resolutions of a nilpotent orbit closure in a classical simple Lie algebra are connected by a finite sequence of diagrams which are locally trivial families of Mukai flops…

This short note provides a symplectic analogue of Vaisman's theorem in complex geometry. Namely, for any compact symplectic manifold satisfying the hard Lefschetz condition in degree 1, every locally conformally symplectic structure is in…

For a smooth Del Pezzo surface the direct sum of global sections of all isomorphism classes of invertible sheaves on it can be almost canonically endowed with a ring structure, called the Cox ring. We show that in characteristic 0 this ring…

We study symplectic varieties defined over fields of positive characteristics, especially the supersingular ones, generalizing the theory of supersingular K3 surfaces. In this work, we are mainly interested in the following two types of…

Symplectic forms taming complex structures on compact manifolds are strictly related to Hermitian metrics having the fundamental form $\partial \bar \partial $-closed, i.e. to strong K\"ahler with torsion (${\rm SKT}$) metrics. It is still…

We show that every negative definite configuration of symplectic surfaces in a symplectic 4--manifold has a strongly symplectically convex neighborhood. We use this to show that, if a negative definite configuration satisfies an additional…

Let $\Gamma$ be a finite subgroup of $\mathrm{Sp}(V)$. In this article we count the number of symplectic resolutions admitted by the quotient singularity $V / \Gamma$. Our approach is to compare the universal Poisson deformation of the…

In "Singularities on Normal Varieties", de Fernex and Hacon started the study of singularities on non-Q-Gorenstein varieties using pullbacks of Weil divisors. In "Log Terminal Singularities", the author of this paper and Urbinati introduce…

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…

We propose the notion of perverse coherent sheaves for symplectic singularities and study its properties. In particular, it gives a basis of simple objects in the Grothendieck group of Poisson sheaves. We show that perverse coherent bases…

In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and…

We study holomorphic spheres in certain symplectic cobordisms and derive information about periodic Reeb orbits in the concave end of these cobordisms from the non-compactness of the relevant moduli spaces. We use this to confirm the strong…

We construct smooth symplectic resolutions of the quotient of R^2 under some infinite discrete sub-group of GL_2(R) preserving a log-symplectic structure. This extends from algebraic geometry to smooth real differential geometry the Du Val…

We study singularity categories through Gorenstein objects in triangulated categories and silting theory. Let ${\omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\mathcal{T}$. We introduce the notion…

In this paper we prove that the Gorenstein cyclic quotient singularities of type \frac 1l (1,..., 1,l-(r-1)) with $l\geq r\geq 2$, have a \textit{unique}torus-equivariant projective, crepant, partial resolution, which is ``full'' iff either…