Related papers: ASK/PSK-correspondence and the r-map

The hyperK\"ahler-quaternionic K\"ahler correspondence constructs quaternionic K\"ahler metrics from hyperK\"ahler metrics with a rotating circle symmetry. We discuss how this may be interpreted as a combination of the twist construction…

We give an explicit formula for the quaternionic K\"ahler metrics obtained by the HK/QK correspondence. As an application, we give a new proof of the fact that the Ferrara-Sabharwal metric as well as its one-loop deformation is quaternionic…

We generalise the hyper-Kahler/quaternionic Kahler (HK/QK) correspondence to include para-geometries, and present a new concise proof that the target manifold of the HK/QK correspondence is quaternionic Kahler. As an application, we…

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…

In the present work, we investigate existence of deformations and algebraic approximability for certain uniruled K\"ahler threefolds. In the first part, we establish existence of infinitesimal deformations for all conic bundles with…

We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special K\"ahler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function.…

We review how a reduction procedure along a principal fibration and an unfolding procedure associated to a suitable momentum map allow to describe the K\"ahler geometry of a finite dimensional complex projective spaces.

It has been shown by Claire Voisin in 2003 that one cannot always deform a compact K\"ahler manifold into a projective algebraic manifold, thereby answering negatively a question raised by Kodaira. In this article, we prove that under an…

We show how affine and projective special K\"ahler manifolds emerge from the structure of quantization. We quantize them and construct natural (wavefunction) representations for the corresponding coherent states. These in turn are shown to…

We give an intrinsic definition of (affine very) special real manifolds and realise any such manifold $M$ as a domain in affine space equipped with a metric which is the Hessian of a cubic polynomial. We prove that the tangent bundle $N=TM$…

We construct the deformation functor associated to a couple of morphisms of differential graded Lie algebras, and use it to study the infinitesimal deformations of a holomorphic map of compact complex manifolds. In particular, in the case…

We associate to the resolved conifold an affine special K\"{a}hler (ASK) manifold of complex dimension 1, and an instanton corrected hyperk\"{a}hler (HK) manifold of complex dimension 2. We describe these geometries explicitly, and show…

We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…

We study symmetry properties of quaternionic K\"ahler manifolds obtained by the HK/QK correspondence. To any Lie algebra $\mathfrak{g}$ of infinitesimal automorphisms of the initial hyper-K\"ahler data we associate a central extension of…

For every compact K\"ahler manifold $X$ of algebraic dimension $a(X) = \dim X - 1$, we prove that $X$ has arbitrarily small deformations to some projective manifolds.

We prove that every projective special K\"ahler manifold with \emph{regular boundary behaviour} is complete and defines a family of complete quaternionic K\"ahler manifolds depending on a parameter $c\ge 0$. We also show that, irrespective…

In this paper we prove that for a complete, connected and oriented K\"{a}ler affine manifold $(M,G)$ of dimension $n,$ if it is K\"ahler affine Ricci flat or the K$\ddot{a}$hler affine scalar curvature $S\equiv0,$ ($n\leq 5$), then the…

We construct a quaternionic-K\"ahler manifold from a conical special K\"ahler manifold with a certain type of mutually-local variation of BPS structures. We give global and local explicit formulas for the quaternionic-K\"ahler metric, and…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…