Sumihiro's theorem
From HandWiki
In algebraic geometry, Sumihiro's theorem, introduced by (Sumihiro 1974), states that a normal algebraic variety with an action of a torus can be covered by torus-invariant affine open subsets. The "normality" in the hypothesis cannot be relaxed.[1] The hypothesis that the group acting on the variety is a torus can also not be relaxed.[2]
Notes
- ↑ Cox, David A.; Little, John B.; Schenck, Henry K. (2011) (in en). Toric Varieties. American Mathematical Soc.. ISBN 978-0-8218-4819-7. https://books.google.com/books?id=AoSDAwAAQBAJ&pg=PA151.
- ↑ "Bialynicki-Birula decomposition of a non-singular quasi-projective scheme." (in en). https://mathoverflow.net/questions/94620/bialynicki-birula-decomposition-of-a-non-singular-quasi-projective-scheme.
References
- Sumihiro, Hideyasu (1974), "Equivariant completion", J. Math. Kyoto Univ. 14: 1–28, doi:10.1215/kjm/1250523277.
External links
- Alper, Jarod; Hall, Jack; Rydh, David (2015). "A Luna étale slice theorem for algebraic stacks". arXiv:1504.06467 [math.AG].
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