07/01/2019, 14:00 — 15:00 — Room P3.10, Mathematics Building
Hugues Auvray, Université Paris-Sud
Complete extremal metrics and stability of pairs on Hirzebruch surfaces
In this talk I will discuss the existence of complete extremal metrics on the complement of simple normal crossings divisors in compact Kähler manifolds, and stability of pairs, in the toric case.
Using constructions of Legendre and Apostolov-Calderbank-Gauduchon, we completely characterize when this holds for Hirzebruch surfaces. In particular, our results show that relative stability of a pair and the existence of extremal Poincaré type/cusp metrics do not coincide. However, stability is equivalent to the existence of a complete extremal metric on the complement of the divisor in our examples. It is the Poincaré type condition on the asymptotics of the extremal metric that fails in general.
This is joint work with Vestislav Apostolov and Lars Sektnan.