Timeline for connectedness of fibers of torus-equivariant moment maps
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2017 at 16:44 | comment | added | Friedrich Knop | I have nothing to say in the singular setting. Also, I assumed that the setting is the algebraic category: algebraic varieties and algebraic forms not necessarily over $\mathbb C$. Also if something doesn't work (like connectedness of fibers) for regular varieties it won't work for singular ones, either. | |
| Oct 30, 2017 at 15:06 | comment | added | user21574 | Closedness of $(1,1)-$ current in singular setting is more complicated see Theorem 1.26, of thichthichiu.files.wordpress.com/2011/07/… . This is a reason that for symplectic variety , we define symplectic form in regular part!. May you add some additional examples in singular setting | |
| Oct 29, 2017 at 20:56 | comment | added | Friedrich Knop | I assumed that $X$ is smooth. Then the pull-back of a symplectic form is clearly symplectic for an étale morphism. | |
| Oct 29, 2017 at 15:49 | comment | added | user21574 | Interesting answer! . In 3. why the pullback of symplectic form is a symplectic form, since as far as I know pullback of symplectic form isnot symplectic(for Kahler form, in the sense of current the pullback is highly non-trivial see arxiv.org/abs/math/0606248). Also you mean form or current? since your example is for non-smooth! | |
| Oct 29, 2017 at 14:04 | vote | accept | Qiao | ||
| Oct 29, 2017 at 10:00 | history | edited | Friedrich Knop | CC BY-SA 3.0 |
added 262 characters in body
|
| Oct 29, 2017 at 9:51 | history | answered | Friedrich Knop | CC BY-SA 3.0 |