Kähler Geometry

Sigma Models, NS-fluxes and Generalized Kähler Geometry

Integrable Systems in Gauge Theory, Kähler Geometry and Super KP Hierarchy – Symmetries and Algebraic Point of View

Symmetries in Generalized Kähler Geometry

We define the notion of amomentmap and reduction in both generalized complex geometry and generalized Kähler geometry. As an application, we give very simple explicit constructions of bi-Hermitian structures on CP , Hirzebruch surfaces, the blow up of CP at arbitrarily many points, and other toric varieties, as well as complex Grassmannians.

Model theory and Kähler geometry

We survey and explain some recent work at the intersection of model theory and bimeromorphic geometry (classification of compact complex manifolds). Included here are the essential saturation of the many-sorted structure C of Kähler manifolds, the conjectural role of hyperkähler manifolds in the description of strongly minimal sets in C, and Campana’s work on the isotriviality of hyperkähler fa...

On the Chern-type problem in Kähler geometry

The purpose of this paper is to investigate the Chern-type problem on Kähler geometry. That is, we study some properties concerning the distribution of the value of the squared norm of the second fundamental form on a complex submanifold of a complex projective space. Mathematics Subject Classification: 53C50, 53C55.

Differential Equations in Special Kähler Geometry

The structure of differential equations as they appear in special Kähler geometry of N = 2 supergravity and (2, 2) vacua of the heterotic string is summarized. Their use for computing couplings in the low energy effective Lagrangians of string compactifications is outlined. Talk presented at the Workshop on String Theory, April 8–10, 1992, Trieste, Italy CERN-TH.6580/92 July 1992