Conjugation on varieties of nilpotent matrices / vorgelegt von Magdalena Boos. 2012
Inhalt
- Introduction
- Theoretical background
- Methods from Algebraic geometry and Invariant theory
- Algebraic group actions
- Invariants and algebraic quotients
- Semi-invariants and GIT-quotients
- Toric varieties
- Representation theory of finite-dimensional algebras
- The concrete setup
- Nilpotency degree 2
- Classification of the orbits
- Homomorphisms, extensions and their combinatorial interpretation
- Closures of Borel orbits
- Minimal, disjoint pieces of degenerations
- Minimal degenerations in general
- Dimensions and the open orbit
- Minimal singularities
- Closures of parabolic orbits
- Finite classifications in higher nilpotency degrees
- Maximal parabolic action for x=3
- Classification of the orbits
- Orbit closures
- Dimensions and the open orbit
- The parabolic subgroup of block sizes (2,2)
- A finiteness criterion
- A wildness criterion
- Generic classification in the nilpotent cone
- Towards an algebraic U-quotient of the nilpotent cone
- A quotient criterion for unipotent actions
- Toric invariants
- Generic separation of the U-orbits
- The toric variety X
- Toric operation(s) on the U-invariant ring
- Explicit description of toric invariants
- Interrelation between N//U and X
- The case n=4
- Towards a GIT-quotient for the Borel action
- The examples n=2 and n=3
- Generic separation of the same weight
- Translation to the language of quiver moduli
- Appendix
- Bibliography