Related papers: Irreducible symplectic complex spaces

The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…

Let $Y$ be a smooth complex projective variety of dimension $N+1$, $L$ an invertible sufficiently ample sheaf, $X\in |L|$ a smooth hypersurface and $\lambda\in F^kH^N(X,C)$ a vanishing cohomology class, where $F^{*}$ is the Hodge filtration…

In this paper we prove the following results: $1)$ We show that any arithmetic quotient of a homogeneous space admits a natural real semi-algebraic structure for which its Hecke correspondences are semi-algebraic. A particularly important…

Let G be a connected reductive group over a non-archimedean local field. We say that an irreducible depth-zero (complex) G-representation is non-singular if its cuspidal support is non-singular. We establish a Local Langlands Correspondence…

We prove a global Torelli theorem for the moduli space of marked triples (X,m,A), consisting of an irreducible holomorphic symplectic manifold X, a marking m of its second integral cohomology, and a stable and rigid sheaf A of Azumaya…

Let $X$ be a compact complex manifold with trivial canonical bundle and satisfying the $\partial\bar{\partial}$-Lemma. We show that the Kuranishi space of $X$ is a smooth universal deformation and that small deformations enjoy the same…

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

We give a classification of irreducible four-dimensional symmetric spaces $G/H$ which admit compact Clifford-Klein forms, where $G$ is the transvection group of $G/H$. For this, we develop a method that applies to particular 1-connected…

We prove various classification results for homogeneous locally conformally symplectic manifolds. In particular, we show that a homogeneous locally conformally Kaehler manifold of a reductive group is of Vaisman type, if the normalizer of…

In this paper we prove the SYZ conjecture for irreducible symplectic varieties that are locally trivial deformation equivalent to moduli spaces of sheaves on K3 surfaces. As an intermediate step in the argument, we generalise to the…

Irreducible symplectic varieties are higher-dimensional analogues of K3 surfaces. In this paper, we prove the Shafarevich conjecture for irreducible symplectic varieties of fixed deformation class. We also observe that the second…

For each positive integer k, we describe a map f from the complex plane to a suitable non-complete complex locally convex space such that f is k times continuously complex differentiable but not k+1 times, and hence not complex analytic. We…

We shall give an example of irreducible symplectic manifolds X and Y which are not bimeromorphic, but have the same periods in the second cohomologies. More explicitly, X and Y are generalized Kummer varieties of dim 4 for a general complex…

Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected base $S$, with everything defined over $\overline{\mathbb{Q}}$. Denote by $\mathbb{V} = R^{2i} f_{*} \mathbb{Z}(i)$ the associated integral…

It is known that irreducible noncommutative differential structures over $\Bbb F_p[x]$ are classified by irreducible monics $m$. We show that the cohomology $H_{\rm dR}^0(\Bbb F_p[x]; m)=\Bbb F_p[g_d]$ if and only if ${\rm Tr}(m)\ne 0$,…

We prove that for any compact toric symplectic manifold, if a Hamiltonian diffeomorphism admits more fixed points, counted homologically, than the total Betti number, then it has infinitely many simple periodic points. This provides a vast…

Let $M\subset{\complex}^n$ be a complex domain of ${\complex}^n$ endowed with a rotation invariant \K form $\omega_{\Phi}= \frac{i}{2} \partial\bar\partial\Phi$. In this paper we describe sufficient conditions on the \K potential $\Phi$ for…

For a symplectic manifold satisfying some topological condition,we define a special class of modules over the deformation quantization algebra. For any two such modules we construct an infinity local system of morphisms. We construct such…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…