Related papers: Holography principle for twistor spaces

Let $X$ be a compact complex manifold such that its canonical bundle $K_X$ is numerically trivial. Assume additionally that $X$ is Moishezon or $X$ is Fujiki with dimension at most four. Using the MMP and classical results in foliation…

In a paper (math.DG/0403528) we obtained explicit examples of Moishezon twistor spaces of some compact self-dual four-manifolds admitting a non-trivial Killing field, and also determined their moduli space. In this note we investigate…

This paper attempts to investigate the space of various characteristic classes for smooth manifold bundles with local system on the total space inducing a finite holonomy covering. These classes are known as twisted higher torsion classes.…

Let $M=P(E)$ be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle $E \to \Sigma$ over a compact complex curve $\Sigma$ of genus $\ge 2$. Building on ideas of Fujiki, we prove that $M$…

Let $X=\overline{X}-D$ be a smooth quasi-projective curve. In arXiv:2110.12300 we constructed a Deligne-Hitchin modui space with Hecke gauge groupoid for connections of rank $2$. We extend this construction to the case of any rank $r$,…

In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and…

A family of irreducible holomorphic symplectic (ihs) manifolds over the complex projective line has unobstructed deformations if its period map is an embedding. This applies in particular to twistor spaces of ihs manifolds. Moreover, a…

Let M be a hyperk\"ahler manifold. The S^2-family of complex structures compatible with the hyperk\"ahler metric can be assembled into a single complex structure on Z=MxS^2; the resulting complex manifold is known as the twistor space of M.…

A Hermitian metric $\omega$ on a complex manifold is called SKT or pluriclosed if $dd^c\omega=0$. Let M be a twistor space of a compact, anti-selfdual Riemannian manifold, admitting a pluriclosed Hermitian metric. We prove that in this case…

In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperk\"ahler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous…

We investigate the structure of smooth holomorphic foliations with numerically flat tangent bundles on compact K\"ahler manifolds. Extending earlier results on non-uniruled projective manifolds by the second and fourth authors, we show that…

We define Hitchin's moduli space for a principal bundle $P$, whose structure group is a compact semisimple Lie group $K$, over a compact non-orientable Riemannian manifold $M$. We use the Donaldson-Corlette correspondence, which identifies…

We study the algebraic dimension of twistor spaces of positive type over $4\bbfP^2$. We show that such a twistor space is Moishezon if and only if its anticanonical class is not nef. More precisely, we show the equivalence of being…

We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open subset of a compact K\"ahler manifold. Our approach…

This article is a contribution to the understanding of the geometry of the twistor space of a symplectic manifold. We consider the bundle $Z$ with fibre the Siegel domain Sp(2n,R)/U(n) existing over any given symplectic 2n-manifold M. Then,…

For any integer $k$ we construct an explicit example of a twistor space which contains a one--parameter family of jumping rational curves, where the normal bundle changes from $O(1)+O(1)$ to $O(k)+O(2-k)$. For $k>3$ the resulting…

A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…

Let M be an almost complex manifold equipped with a Hermitian form such that its de Rham differential has Hodge type (3,0)+(0,3), for example a nearly Kahler manifold. We prove that any connected component of the moduli space of…

We study the geometry of the twistor space of the universal hyperkaehler implosion Q for SU(n). Using the description of Q as a hyperkaehler quiver variety, we construct a holomorphic map from the twistor space Z_Q of Q to a complex vector…

Let $M$ be a compact hyperkahler manifold equipped with a Lagrangian fibration $\pi:\; M \to X$, and $M'$ the smooth locus of $\pi$. We prove that over a complement to a codimension $\geq 2$ subset in $X$, the projection $\pi:\; M' \to X$…