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.
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