Lecture Notes from Courses
Algebraic Transformation Groups – An Introduction
(Version from January 2017)
These are some notes from several courses on "Algebraic Transformation Groups and Invariant Theory". They are still incomplete, but should eventually be published as a book.
Fiber Bundles, Slice Theorem and Applications
These are notes from some lectures I gave in the Fall 2015.
Algebraic Geometry – An Introduction
(Version from July 2014)
Notes from several courses on "Algebraic Geometry". The text will eventually become the first appendix of a book "Algebraic Transformation Groups". Other chapters are also available on this site.
Classical Invariant Theory – A Primer (with Claudio Procesi)
(Version from July 1996)
These are notes from courses given in Basel, based on some lecture notes of Claudio Procesi
We discuss and prove some results about the Lie algebra of vector fields Vec(X) on an affine variety X which are due to J. Grabowski and T. Siebert, e.g. that two normal varieties X and Y are isomorphic if and only if the vector fields Vec(X) and Vec(Y) are isomorphic Lie algebras.
We give a modern proof of the Regularization Theorem of A. Weil which says that for every rational action of an algebraic group G on a variety X there exist a variety Y with a regular G-action and a G-equivariant birational map X ---> Y. Moreover, we show that a rational G-action on an affine variety X with the property that each element g from a dense subgroup of G induces a regular automorphism of X, is a regular action.
Eine nicht ganz ernste "mathematische" Kurzgeschichte!