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Automorphism Groups of Algebraic Varieties: Geometry, Combinatorics, and Representations
| Third-party funded project |
| Project title |
Automorphism Groups of Algebraic Varieties: Geometry, Combinatorics, and Representations |
| Principal Investigator(s) |
Kraft, Hanspeter
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| Organisation / Research unit |
Departement Mathematik und Informatik / Algebra (Kraft) |
| Project Website |
http://www.math.unibas.ch/kraft |
| Project start |
01.04.2012 |
| Probable end |
31.03.2014 |
| Status |
Completed |
| Abstract |
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?
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| Keywords |
algebraic groups, automorphism groups, endomorphisms, flexible varieties, infinite transitivity, ind-groups, ind-varieties, representations |
| Financed by |
Swiss National Science Foundation (SNSF)
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| Follow-up project of |
247416 Computational and Combinatorial Methods for Algebraic Group Actions
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01/05/2024
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