Blowing up extremal Poincaré type manifolds

Geometry/topology Seminar

Lars Sektnan (CIRGET)

Monday, April 3, 2017 -
3:15pm to 4:15pm
119 Physics

One of the central conjectures in Kähler geometry is the Yau-Tian-Donaldson conjecture relating the existence of canonical Kähler metrics to algebro-geometric stability. A natural question is to ask what happens when such a metric does not exist, and here Kähler metrics of Poincaré type are expected to play an important role. These metrics are Kähler metrics defined on the complement of a divisor in a compact complex manifold and have a cusp-like singularity near the divisor. The blow-up theorem of Arezzo-Pacard and its generalizations give sufficient conditions for the blow-up of a compact Kähler manifold admitting a canonical metric to also carry such a metric. I will describe an extension of this result to the Poincaré type setting.

Last updated: 2017/09/19 - 6:58pm