Related papers: Complex structures on product of circle bundles ov…

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…

We determine the 6-dimensional solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong K\"ahler with torsion…

It is shown that every bundle $\varSigma\to M$ of complex spinor modules over the Clifford bundle $\Cl(g)$ of a Riemannian space $(M,g)$ with local model $(V,h)$ is associated with an lpin ("Lipschitz") structure on $M$, this being a…

The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…

We describe the first order moduli space of heterotic string theory compactifications which preserve $N=1$ supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we…

By virtue of the well-known theorem, a structure Lie group K of a principal bundle $P$ is reducible to its closed subgroup H iff there exists a global section of the quotient bundle P/K. In gauge theory, such sections are treated as Higgs…

In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description we explicitly classify homogeneous l.c.K. structures on…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

The Corlette-Donaldson-Hitchin-Simpson's correspondence states that, on a compact K\"ahler manifold $(X, \omega )$, there is a one-to-one correspondence between the moduli space of semisimple flat complex vector bundles and the moduli space…

We review the theory of quaternionic Kahler and hyperkahler structures. Then we consider the tangent bundle of a Riemannian manifold M with a metric connection D (with torsion) and with its well estabilished canonical complex structure.…

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

We construct a generalization of twistor spaces of hypercomplex manifolds and hyper-Kahler manifolds $M$, by generalizing the twistor $\mathbb{P}^{1}$ to a more general complex manifold $Q$. The resulting manifold $X$ is complex if and only…

A new class of compact K\"ahler manifolds, called special, is defined, which are the ones having no surjective meromorphic map to an orbifold of general type. The special manifolds are in many respect higher-dimensional generalisations of…

A principal torus bundle over a complex manifold with even dimensional fiber and characteristic class of type $(1,1)$ admits a family of regular generalized complex structures (GCS) with the fibers as leaves of the associated symplectic…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

The projective variety of square-zero elements in the six-dimensional minimal supersymmetry algebra is isomorphic to $\mathbb{P}^1 \times \mathbb{P}^3$. We use this fact, together with the pure spinor superfield formalism, to study…

Let G be a simple and simply connected complex linear algebraic group. In this paper, we discuss the generalization of the parabolic construction of holomorphic principal G-bundles over a smooth elliptic curve to the case of a singular…

Let X be a separated finite type scheme over a noetherian base ring K. There is a complex C(X) of topological O_X-modules on X, called the complete Hochschild chain complex of X. To any O_X-module M - not necessarily quasi-coherent - we…

Given an N=2 supersymmetric field theory in four dimensions, its dimensional reduction on S^1 is a sigma model with hyperkahler target space M. We describe a canonical line bundle V on M, equipped with a hyperholomorphic connection. The…

Let (M,I) be a compact Kaehler manifold admitting a hypercomplex structure. We show that (M, I) admits a natural HKT-metric. This is used to construct a holomorphic symplectic form on (M,I).