Timeline for Research of a reference about $G$-linearizations of line bundles on quasi-projective schemes
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 9, 2014 at 22:46 | comment | added | Yemon Choi | It seems to me that these comments could be left as answers | |
| Aug 9, 2014 at 14:46 | review | Close votes | |||
| Aug 10, 2014 at 4:07 | |||||
| Aug 9, 2014 at 14:34 | comment | added | Olivier Benoist | abx's comment immediately provides counterexamples when $G$ is not connected. There are also counterexamples when $G$ is connected and $X$ not normal, but none if $G$ is connected and $X$ is normal : see question mathoverflow.net/questions/109310/… , its answer and the references therein. | |
| Aug 9, 2014 at 14:29 | comment | added | abx | You forgot an obvious necessary condition, namely that some power $L^m$ of $L$ should be $G$-invariant (i.e. $g^*L^m\cong L^m$ for all $g$ in $G$). That this is equivalent to your statement is Proposition 1.5 in Mumford's GIT. | |
| Aug 9, 2014 at 14:25 | history | edited | User3773 | CC BY-SA 3.0 |
added 273 characters in body
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| Aug 9, 2014 at 13:58 | history | asked | User3773 | CC BY-SA 3.0 |