16 feb 2016 -- 16:00
Aula Dal Passo, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
Grauert proved in 1958 that every continuous section of a holomorphic principal G-bundle over a Stein space can be deformed to a holomorphic section. Here, G is any complex Lie group. Starting with Gromov’s seminal paper in 1989, Grauert’s theorem has been extended to much more general bundles. I will describe recent joint work with Frank Kutzschebauch (Bern) and Gerald Schwarz (Brandeis) in which we adapt Grauert’s theorem to certain “bundles” that arise naturally in geometric invariant theory but can be badly singular. This work has applications to the so-called linearisation problem for group actions on affine spaces. I will give plenty of background; in particular, I will not assume any familiarity with geometric invariant theory.