Sumihiro's theorem

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

  1. ↑
  2. ↑ http://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 .


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