Observability in invariant theory
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- by Lex E. Renner PDF
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Abstract:
We consider actions $G\times X\to X$ of the affine, algebraic group $G$ on the affine, algebraic variety $X$. We say that $G\times X\to X$ is observable in codimension one if for any height-one, $G$-invariant, prime ideal $\mathfrak {p}\subset k[X]$, $\mathfrak {p}^G\neq (0)$. Many familiar actions are observable in codimension one. We characterize such actions geometrically and indicate how they fit into the general framework of invariant theory. We look at what happens if we impose further restrictions, such as $G$ being reductive or $X$ being factorial. We indicate how Grosshans subgroups are involved.References
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Additional Information
- Lex E. Renner
- Affiliation: Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7, Canada
- Received by editor(s): March 8, 2011
- Received by editor(s) in revised form: May 31, 2011, and June 22, 2011
- Published electronically: May 24, 2012
- Communicated by: Harm Derksen
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 205-216
- MSC (2010): Primary 13A50, 14L30
- DOI: https://doi.org/10.1090/S0002-9939-2012-11321-8
- MathSciNet review: 2988723