Speaker: Lars Martin Sektnan (Chalmers Institute of Technology and University of Gothenburg)
Title: Constant scalar curvature Kähler metrics and semistable vector bundles
When: Wednesday, November 6, at 10:00
Where: Room 147 in VR-II
Abstract: A central question in Kähler geometry is if a Kähler manifold admits a canonical metric, such as a Kähler-Einstein metric or more generally a constant scalar curvature Kähler (cscK) metric, in a given Kähler class. The Yau-Tian-Donaldson conjecture predicts that this is equivalent to an algebraic notion of stability. In this talk, I will discuss a necessary and sufficient condition for the projectivisation of a slope semistable vector bundle to admit cscK metrics in adiabatic classes, when the base admits a cscK metric. In particular, this shows that the existence of cscK metrics is equivalent to K-stability in this setting. Moreover, our construction reduces K-stability to a finite dimensional criterion in terms of intersection numbers associated to the vector bundle. This is joint work with Annamaria Ortu.