Bubbling of Kahler-Einstein metrics: examples and conjectures

Time：2023-12-5, Tuesday 21:00 - 22:00

Venue：Zoom Meeting ID: 271 534 5558 Passcode: YMSC

Organizer：Jialong Deng, Akito Futaki

Speaker：Martin de Borbon Loughborough University

Zoom link：

https://us06web.zoom.us/j/2715345558?pwd=eXRTTExpOVg4ODFYellsNXZVVlZvQT09

Abstract：

I will report on joint work with Cristiano Spotti. Chi Li's theory of normalized volumes permits the algebraic determination of tangent cones of singular Kahler-Einstein metrics. The general principle is to extend this to the dynamic setting of families and determine all possible rescaled limits using algebraic geometry. I will discuss examples in low dimensions, including polyhedral metrics on the sphere and Kahler-Einstein metrics on complex surfaces with cone singularities along curves.

DATEDecember 5, 2023

Related News

0
Stability of Einstein metrics
AbstractEinstein metrics can be characterised as critical points of the (normalised) total scalar curvature functional. They are always saddle points. However, there are Einstein metrics which are local maxima of the functional restricted to metrics of fixed volume and constant scalar curvature. These are by definition stable Einstein metrics. Stability can equivalently be characterised by a sp...
1
Einstein metrics from Derdziński duality
Abstract：(joint work with Rosa Sena-Dias) A theorem of Derdziński from the 1980's establishes that certain Einstein metrics are conformal to Bach-flat extremal Kahler metrics. Using this result Rosa Sena-Dias and I classified conformally Kähler, U(2)-invariant, Einstein metrics on the total space of O(−m). This yields infinitely many 1-parameter families of metrics exhibiting several differe...