Related papers: Complex manifolds with split tangent bundle

Given a projective morphism of compact, complex, algebraic varieties and a relatively ample line bundle on the domain we prove that a suitable choice, dictated by the line bundle, of the decomposition isomorphism of the Decomposition…

Let $(M^n, g)$ be a compact K\"ahler manifold with nonpositive bisectional curvature. We show that a finite cover is biholomorphic and isometric to a flat torus bundle over a compact K\"ahler manifold $N^k$ with $c_1 < 0$. This confirms a…

Let $X$ be a $\mathbb Q$-Fano variety admitting a K\"ahler-Einstein metric. We prove that up to a finite quasi-\'etale cover, $X$ splits isometrically as a product of K\"ahler-Einstein $\mathbb Q$-Fano varieties whose tangent sheaf is…

Let X be a compact connected Riemann surface of genus g > 0 equipped with a nonzero holomorphic 1-form. Let M denote the moduli space of semistable Higgs bundles on X of rank r and degree r(g-1)+1; it is a complex symplectic manifold. Using…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

Let G be compact Lie group. It is shown that the cotangent bundle of the complexification of G admits a hyperkahler structure which is invariant under left and right translations by elements of G. The proof is to realize the cotangent…

A linear F-manifold is an F-manifold (E, \circ , e) defined on the total space of a vector bundle \pi : E \rightarrow M for which the multiplication and unit field are linear tensor fields. We develop a systematic treatment of linear…

Generalising a classical theorem by Ueno, we prove structure results for manifolds with nef or semiample cotangent bundle.

This paper is motivated by Grothendieck's splitting theorem. In the 1960s, Gohberg generalized this to a class of Banach bundles. We consider a compact complex manifold $X$ and a holomorphic Banach bundle $E \to X$ that is a compact…

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on…

In this paper we obtain an explicit formula for the number of hypersurfaces in a compact complex manifold X (passing through the right number of points), that has a simple node, a cusp or a tacnode. The hypersurfaces belong to a linear…

The purpose of this paper is to translate positivity properties of the tangent bundle (and the anti-canonical bundle) of an algebraic manifold into existence and movability properties of rational curves and to investigate the impact on the…

The structure of topological quantum field theories on the compact Kahler manifold is interpreted. The BRST transformations of fields are derived from universal bundle and the observables are found from the second Chern class of universal…

Let $P(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal K\"ahler metric on the ruled manifold $P(E)$ in terms of relative K-polystability and the…

We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.

Following Simpson we consider the integrable system structure on the moduli spaces of Higgs bundles on a compact K\"ahler manifold $X$. We propose a description of the corresponding spectral cover of $X$ as the fiberwise projective dual to…

In an earlier paper we conjectured a relation between the quantum $\mathcal D$-modules of a smooth variety $X$ and the projectivisation of a direct sum of line bundles over it. In this paper we prove the conjecture when $X$ is a complete…

We show that a compact Kahler manifold admitting a nondegenerate holomorphic 2-form valued in a line bundle is a finite cyclic cover of a hyperkahler manifold. With respect to the connection induced by the locally hyperkahler metric, the…

We first give a deformation theory of integrable distributions of codimension 1. We define a parametrization of families of smooth hypersurfaces near a Levi flat hypersurface L such that the Levi flat deformations are given by the solutions…

Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings. We study the variety of unitary representations of the fundamental group of U with certain restrictions related to the divisor. We show that…