Related papers: Compact tori associated to hyperkaehler manifolds …

We define Hodge correlators for a compact Kahler manifold X. They are complex numbers which can be obtained by perturbative series expansion of a certain Feynman integral which we assign to X. We show that they define a functorial real…

We study Fourier-Mukai equivalence of K3 surfaces in positive characteristic and show that the classical results over the complex numbers all generalize. The key result is a positive-characteristic version of the Torelli theorem that uses…

We exhibit many examples of closed symplectic manifolds on which there is an autonomous Hamiltonian whose associated flow has no nonconstant periodic orbits (the only previous explicit example in the literature was the torus T^2n (n\geq 2)…

We determine the Hamiltonian vector field on an odd dimensional manifold endowed with almost cosymplectic structure. This is a generalization of the corresponding Hamiltonian vector field on manifolds with almost transitive contact…

In this paper, we establish a structure theorem for a smooth projective variety $X$ with semi-positive holomorphic sectional curvature. Our structure theorem contains the solution for Yau's conjecture and it can be regarded as a natural…

Given a $k$--scheme $X$ that admits a tilting object $T$, we prove that the Hochschild (co-)homology of $X$ is isomorphic to that of $A= End_{X}(T)$. We treat more generally the relative case when $X$ is flat over an affine scheme $Y=\Spec…

We define the theta group associated to a simple coherent sheaf $\cal F$ on a hyperk\"ahler manifold $X$ of Kummer type or OG6 type, provided $g^{*}({\cal F})$ is isomorphic to $\cal F$ for every automorphism $g$ of $X$ acting trivially on…

We construct a K3 surface whose transcendental lattice has a self-isomorphism which is not a linear combination of self-isomorphisms over $\mathbb{Q}$ which preserve cup products up to nonzero multiples. Products of it with itself give…

We prove that the integral cohomology ring modulo torsion $H^*(\mathrm{Sym}^n X;\mathbb{Z})/\mathrm{Tor}$ for the symmetric product of a connected CW-complex $X$ of finite homology type is a functor of $H^*(X;\mathbb{Z})/\mathrm{Tor}$ (see…

We show that under the hypotheses of Strominger, Yau and Zaslow's paper, a mirror partner of a K3 surface $X$ with a fibration in special Lagrangian tori can be obtained by rotating the complex structure of $X$ within its hyperk\"ahler…

This thesis contains work which appeared in several papers. Additionally to the results in the papers it contains a detailed introduction and some further proofs and remarks. The dissertation gives a description of the topology and…

In this thesis we have proved a conjecture about the moduli space SU_X(3) of semi-stable rank 3 vector bundles with trivial determinant on a genus 2 curve X, due to I. Dolgachev. Given X a smooth projective curve of genus 2, and the…

In this note we study two features of submanifolds (subvarieties) with ample normal bundles in a compact K\"ahler manifold X. First, we study how algebraic X can be, i.e. we investigate the algebraic dimension. Second, we study curves with…

New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is…

Let $X$ be a compact Riemann surface, $\Sigma$ a finite set of points and $M = X\setminus \Sigma$. We study the $L^2$ cohomology of a polarized complex variation of Hodge structure on a Galois covering of the Riemann surface of finite type…

For a smooth projective unitary representation of a locally convex Lie group G, the projective space of smooth vectors is a locally convex Kaehler manifold. We show that the action of G on this space is weakly Hamiltonian, and lifts to a…

Let M be a compact Riemannian manifold equipped with a parallel differential form \omega. We prove a version of Kaehler identities in this setting. This is used to show that the de Rham algebra of M is weakly equivalent to its subquotient…

We use a result of van Geemen to determine the endomorphism algebra of the Kuga--Satake variety of a K3 surface with real multiplication. This is applied to prove the Hodge conjecture for self-products of double covers of $\PP^2$ which are…

Let $X$ be a Calabi-Yau threefold. A conifold transition first contracts $X$ along disjoint rational curves with normal bundles of type $(-1,-1)$, and then smooth the resulting singular complex space $\bar{X}$ to a new compact complex…

We construct projectors in the ring of correspondences of a complex uniruled 3-fold $X$ which lift the Kuenneth components of the diagonal in singular cohomology and have other properties which were conjectured by J. Murre. Such Murre…