Related papers: Stable Bundles on Irregular Vaisman Manifolds

Let $(M,g)$ be a Riemannian manifold, $L(M)$ be its frame bundle, $O(M)$ its orthonormal frame bundle. For a distribution $D$ on $M$ we define a subbundle $L(D)\subset L(M)$ or $O(D)\subset O(M)$ in a natural way. This allows us to consider…

We characterize the existence of a locally conformally K\"ahler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for K\"ahler metrics.

This paper considers the links between the geometry of the various flag manifolds of loop groups and bundles over families of rational curves. Aa an application, a stability result for the moduli on a rational ruled surface of G-bundles…

We prove that any Kaehler manifold admitting a flat complex conformal connection is a Bochner-Kaehler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain…

In this paper we show that in a stable range the cohomology of the space of regular algebraic sections of a line bundle $\mathscr{L}$on a curve $X$ is isomorphic to the cohomology of the space of regular $C^{\infty}$sections of the same…

We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…

We consider actions of reductive complex Lie groups $G=K^C$ on K\"ahler manifolds $X$ such that the $K$--action is Hamiltonian and prove then that the closures of the $G$--orbits are complex-analytic in $X$. This is used to characterize…

Given a compact K\"ahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of…

This article contains a compression of results from alg-geom/9501001, with most proofs omitted. We prove that every two points of the connected moduli space of holomorphically symplectic manifolds can be connected with so-called ``twistor…

In this paper, we study the moduli spaces $\mathcal{M}_{\delta,c_2}$ of stable rank-2 vector bundles on non-K\" ahler elliptic surfaces, thus giving a classification these bundles; in the case of Hopf and Kodaira surfaces, these moduli…

For an abelian surface $A$, we consider stable vector bundles on a generalized Kummer variety $K_n(A)$ with $n>1$. We prove that the connected component of the moduli space which contains the tautological bundles associated to line bundles…

We study compact locally homogeneous plane waves. Such a manifold is a quotient of a homogeneous plane wave $X$ by a discrete subgroup of its isometry group. This quotient is called standard if the discrete subgroup is contained in a…

A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's…

We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian…

We obtain a class of locally symmetric Kaehler Einstein structures on the cotangent bundle of a Riemannian manifold of negative sectional curvature. Similar results are obtained in the case of a Riemannian manifold of positive sectional…

We consider a manifold X obtained by a Kahler reduction of C^n, and we define its hyperkahler analogue M as a hyperkahler reduction of T^*C^n = H^n by the same group. In the case where the group is abelian and X is a smooth toric variety, M…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…

In this paper, we study holomorphic vector bundles on (diagonal) Hopf manifolds. In particular, we give a description of moduli spaces of stable bundles on generic (non-elliptic) Hopf surfaces. We also give a classification of stable rank-2…

We prove the existence of at least $cl(M)$ periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold $M$. These Hamiltonians are not necessarily convex but they satisfy a certain…

Let $G/H$ be a contractible homogeneous Sasaki manifold. A compact locally homogeneous aspherical Sasaki manifold $\Gamma\big\backslash G/H$ is by definition a quotient of $G/H$ by a discrete uniform subgroup $\Gamma\leq G$. We show that a…