STRATIFICATIONS ASSOCIATED TO REDUCTIVE GROUP ACTIONS ON AFFINE SPACES
| Autor: | Victoria Hoskins |
|---|---|
| Přispěvatelé: | University of Zurich, Hoskins, V |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Pure mathematics General Mathematics Reductive group 142-005 142-005 Stratification (mathematics) Mathematics - Algebraic Geometry Mathematics - Symplectic Geometry Lie algebra FOS: Mathematics Affine space Symplectic Geometry (math.SG) Geometric invariant theory Invariant (mathematics) Algebraic Geometry (math.AG) Moment map Maximal compact subgroup 2600 General Mathematics Mathematics |
| Popis: | For a complex reductive group G acting linearly on a complex affine space V with respect to a character, we show two stratifications of V associated to this action (and a choice of invariant inner product on the Lie algebra of the maximal compact subgroup of G) coincide. The first is Hesselink's stratification by adapted 1-parameter subgroups and the second is the Morse theoretic stratification associated to the norm square of the moment map. We also give a proof of a version of the Kempf-Ness theorem which states that the GIT quotient is homeomorphic to the symplectic reduction (both taken with respect to the character). Finally, for the space of representations of a quiver of fixed dimension, we show that the Morse theoretic stratification and Hesselink's stratification coincide with the stratification by Harder-Narasimhan types. 24 pages |
| Databáze: | OpenAIRE |
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