Geometry/Topology Seminar
Lars Sektnan
Gothenburg
Blowing up extremal Kähler manifolds
Abstract: Extremal Kähler metrics were introduced by Calabi in the 80’s as a type of canonical Kähler metric on a Kähler manifold, and are a generalisation of constant scalar curvature Kähler metrics in the case when the manifold admits automorphisms. A natural question is when the blowup of a manifold in a point admits an extremal Kähler metric. For classes where the volume of the exceptional divisor is small, we completely settle the question in terms of a finite dimensional moment map/GIT condition, generalising work of Arezzo-Pacard, Arezzo-Pacard-Singer and Székelyhidi. Our methods also allow us to deal with a certain semistable case that has not been considered before, where the original manifold does not admit an extremal metric, but is infinitesimally close to doing so. As a consequence of this, we solve the first non-trivial special case of a conjecture of Donaldson. This is joint work with Ruadhaí Dervan.
Wednesday November 9, 2022 at 3:00 PM in 636 SEO