Timeline for Cover by $K$-invariant affine open sets
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2020 at 18:59 | comment | added | Angelo | Homogenous varieties under a connected reductive group are another class of examples. | |
| Sep 1, 2020 at 17:12 | comment | added | Dave Anderson | ...and Jason's example also gives a counterexample to the OP's more general question: this action of K does not extend to an algebraic action of K_C, at least if one complexifies to a split algebraic torus. | |
| Sep 1, 2020 at 16:48 | comment | added | Jason Starr | No, that is not true. Let $X$ be a complex Abelian variety of complex dimension $g>0$, and let $K$ be the underlying real Lie group of $X$ considered as a product of $2g$ copies of the real Lie group $U(1)$. The only $K$-invariant open subsets are the empty set and all of $X$. | |
| Sep 1, 2020 at 11:36 | history | asked | Simon Parker | CC BY-SA 4.0 |