Generalized orthotoric Kähler surfaces

Kähler Surfaces And

A complex ruled surface admits an iterated blow-up encoded by a parabolic structure with rational weights. Under a condition of parabolic stability, one can construct a Kähler metric of constant scalar curvature on the blow-up according to [18]. We present a generalization of this construction to the case of parabolically polystable ruled surfaces. Thus we can produce numerous examples of Kähle...

Ricci Flow on Kähler-einstein Surfaces

Scalar-flat Kähler Surfaces of All Genera

Let (M,J) be a compact complex 2-manifold which which admits a Kähler metric for which the integral of the scalar curvature is nonnegative. Also suppose that M does not admit a Ricci-flat Kähler metric. Then if M is blown up at sufficiently many points, the resulting complex surface (M̃ , J̃) admits Kähler metrics with scalar curvature identically equal to zero. This proves Conjecture 1 of [16]. ...

0 Ricci flow on Kähler - Einstein surfaces

Kähler (& Hyper-kähler) Manifolds

These notes are based on two talks given at the Arithmetic & Algebraic Geometry Seminar of the Korteweg-de Vriesinstituut for mathematics of the Universiteit van Amsterdam. They are intended to give a short introduction to the theory of Kähler manifolds, with a slight focus of applicability to the subject of K3 surfaces. However, they also include other interesting results not related to K3 sur...