KASS-seminarium

Abstrakt finns enbart på engelska: To understand a compact Kähler manifold X, it is often helpful to study its degenerations. The idea of non-Archimedean (n-A) Kähler geometry is to think of such degenerations as Kähler metrics on an associated n-A space. The n-A Monge-Ampère measure of a degeneration is then supposed to encode how the volume of X distributes as X degenerates.

My aim of this talk is to give a brief and gentle introduction to n-A Kähler geometry, seen from a Kähler geometric perspective, rather than the more traditional algebro-geometric perspective. In particular I will discuss a Calabi-Yau theorem in this setting, first proved in the algebraic case by Sébastien Boucksom and Mattias Jonsson (building on earlier work of Sébastien Boucksom, Charles Favre and Mattias Jonsson), and subsequently proved in the general Kähler case by Pietro Mesquita-Piccione and myself.

Prior knowledge expected: the definitions of a Kähler manifold/metric/form/class and to know what the blow-up of a complex submanifold means.