Related papers: K\"ahler geometry on complex projective spaces via…
The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…
We show how certain topological properties of co-K\"ahler manifolds derive from those of the K\"ahler manifolds which construct them. In particular, we show that the existence of parallel forms on a co-K\"ahler manifold reduces the…
We prove the convergence of geodesic distance during the quantization of the space of K\"ahler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.
We study the hyperkaehler geometry of a regular semisimple adjoint orbit of SL(k,C) via the algebraic geometry of the corresponding reducible spectral curve.
We prove that the space of convex real projective structures on a surface of genus $g\ge 2$ admits a mapping class group invariant K\"ahler metric where Teichm\"uller space with Weil-Petersson metric is a totally geodesic complex…
The K\"ahler cone of a compact manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We write down the curvature tensor of this metric by embedding the K\"ahler cone in the space of…
We prove that every compact K\"ahler threefold has arbitrarily small deformations to some projective manifolds, thereby solving the Kodaira problem in dimension 3.
Given a holomorphic Lagrangian fibration of a compact hyperkahler manifold, we use the differential geometry of the special Kahler metric that exists on the base away from the discriminant locus, and show that the pullback of the tangent…
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K\"ahler manifold case. We find conditions for the information geometry of linear systems to be…
In the presence of classical phase space singularities the standard methods are insufficient to attack the problem of quantization.In certain situations the difficulties can be overcome by means of K\"ahler quantization on stratified…
The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the…
A symplectically invariant definition of special K\"ahler geometry is discussed. Certain aspects hereof are illustrated by means of Calabi-Yau moduli spaces.
We study compact K\"ahler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this…
The recently established metric reduction in generalized geometry is encoded in 0-dimensional supersymmetric $\sigma$-models. This is an example of balanced topological field theories. To find the geometric content of such models, the…
Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of…
Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an…
We give some remarks on geodesics in the space of K\"ahler metrics that are defined for all time. Such curves are conjecturally induced by holomorphic vector fields, and we show that this is indeed so for regular geodesics, whereas the…
We investigate several topics of the geometry on real Cayley-Klein spaces. An important concern for us is to define a distance function on the projective space in such a way that the distance between two anisotropic subspaces of the same…
The paper is part of an attempt of understanding non-K\"ahler threefolds. We start by looking at compact complex non-K\"ahler threefolds with algebraic dimension two and admitting locally conformally K\"ahler metrics. Under certain…
It has been often observed that K\"ahler geometry is essentially a $U(1)$ gauge theory whose field strength is identified with the K\"ahler form. However it has been pursued neither seriously nor deeply. We argue that this remarkable…