Forschungsseminar: Komplexe Geometrie

22.06.2012 Mustafa Kalafat (METU Ankara)

Algebraic geometric techniques in differential geometry

Abstract: We will discuss how tools from Algebraic Geometry can be used to solve problems in Differential Geometry, and discuss some of the relationships between these two fields. In particular, we will first concentrate on self-dual metrics on 4-Manifolds. We prove that the connected sum of two self-dual Riemannian 4-manifolds of positive scalar curvature is again a self-dual Riemannian manifold of positive scalar curvature, under a vanishing hypothesis. The proof involves Kodaira-Spencer-Freedman deformation theory and the Leray spectral sequence. If time permits we will discuss metrics on quotients of Enriques Surfaces, and applications of geometric invariant theory, complex/almost complex and Kahler structures. At least the first half of the talk will be elementary and be accessible to the general audience.