Automorphism Groups of Algebraic Varieties: Geometry, Combinatorics, and Representations
Research Project
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01.04.2012
- 31.03.2014
The object of this research proposal is the automorphism group Aut(X) of an (affine) algebraic variety X, i.e. the group of regular automorphisms of X. A lot is known for curves, but almost nothing in higher dimension. The only case is the affine Cremona group GA(n) := Aut(C^n), the automorphism group of affine n-space which got a lot of attention in recent years. It also appears in some of our research projects. The main goal of this research project is to understand the relation between the structure of the automorphism group Aut(X) and the variety X: Basic Problem. How much does the automorphism group Aut(X) of an affine variety X determine the structure of X?