Sumihiro's theorem explained

In algebraic geometry, Sumihiro's theorem, introduced by, 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]

References

• .

External links

• 1504.06467. Alper. Jarod. A Luna étale slice theorem for algebraic stacks. Hall. Jack. Rydh. David. math.AG. 2015.

Notes and References

1. Book: Cox, David A. . Toric Varieties . Little . John B. . Schenck . Henry K. . 2011 . American Mathematical Soc. . 978-0-8218-4819-7 . en.
2. Web site: Bialynicki-Birula decomposition of a non-singular quasi-projective scheme. . 2023-03-10 . MathOverflow . en.