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Observability in invariant theory II: Divisors and rational invariants


Author: Lex E. Renner
Journal: Proc. Amer. Math. Soc. 143 (2015), 4113-4121
MSC (2010): Primary 13A50, 14L30
DOI: https://doi.org/10.1090/proc/12804
Published electronically: June 16, 2015
MathSciNet review: 3373912
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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''?


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Additional Information

Lex E. Renner
Affiliation: Department of Mathematics, Western University, London, Ontario, Canada N6A 5B7
Email: lex@uwo.ca

DOI: https://doi.org/10.1090/proc/12804
Received by editor(s): October 6, 2013
Published electronically: June 16, 2015
Communicated by: Harm Derksen
Article copyright: © Copyright 2015 American Mathematical Society

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