Observability in invariant theory II: Divisors and rational invariants
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Abstract:
Let $G\times X\to X$ be an action of the connected algebraic group $G$ on the irreducible, affine variety $X$. We discuss the relationship between $[k[X]^G]$ and $k(X)^G$, where $[k[X]^G]$ denotes the quotient field of $k[X]^G$. We are particularly interested in the following three questions. (1) When is the inclusion $[k[X]^G]\subseteq k(X)^G$ a finite extension of fields? (2) What is the role of $G$-invariant divisors? (3) What is the exact characterization of “observable in codimension one”?References
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Additional Information
- Lex E. Renner
- Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
- Email: lex@uwo.ca
- Received by editor(s): October 6, 2013
- Published electronically: June 16, 2015
- Communicated by: Harm Derksen
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 4113-4121
- MSC (2010): Primary 13A50, 14L30
- DOI: https://doi.org/10.1090/proc/12804
- MathSciNet review: 3373912