Abstracts

Daniel Greb, Uniformisation of higher-dimensional singular varieties
References Abstract ± The aim of the lectures is to explain how methods related to sheaf-theoretic stability help to understand the structure of higher-dimensional, potentially singular projective varieties. After discussing basics of stability for sheaves and after introducing the main classes of singularities one has to deal with in the Minimal Model Program, I will discuss flatness criteria for semistable sheaves on singular varieties and apply these criteria to obtain a characterisation finite quotients of projective spaces.

Henri Guenancia, Application of Kähler-Einstein metrics in Algebraic Geometry
Abstract ±

Andreas Höring, Positivity of (co)tangent bundles
Abstract ± Summary : Let \(X\) be a projective manifold. While the positivity of the (anti)canonical bundle has been discussed from various angles and is the central object of the minimal model program, the positivity of the (co)tangent bundle remains somewhat mysterious and difficult to check in practice. In this series of talks I will discuss some recent work where we try to determine the interaction between the pseudoeffectivity of the (co)tangent bundle and the global geometry of \(X\).
Outline of the talks:
Talk 1 : Setup, first examples and open problems Talk 2 : Elliptic surfaces Talk 3 : del Pezzo manifolds

Christian Lehn, TBA
Abstract ±