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# Invariant rings of reductive representations and singularities of the Minimal Model Program

## June 1 at 16:00 – 17:00 CEST

Oberseminar Algebra und Geometrie

Daniel Greb (Univ. Duisburg-Essen)

Abstract:

I will discuss my recent work with Braun, Langlois, and Moraga showing that invariant rings of finite-dimensional representations of (linearly) reductive groups over an algebraically closed field of characteristic zero have Kawamata log-terminal (klt) singularities. I will spend most of the time on explaining what klt singularities are, why the klt condition is a very natural and geometric condition, and why smaller classes of singularities are not sufficient in order to understand arbitrary reductive quotient singularities. Then, I will discuss some applications of the main result, e.g. to varieties important in geometric representation theory and to certain moduli spaces. If time permits, I will discuss some ideas of the proof.