Timeline for Twists of projective automorphisms
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2015 at 17:26 | vote | accept | Daniel Loughran | ||
| Mar 29, 2015 at 17:25 | answer | added | Daniel Loughran | timeline score: 1 | |
| Mar 24, 2015 at 5:03 | comment | added | naf | I should have assumed that $X$ is non-degenerate (so there is at most one automorphism of $\mathbb{P}^n$ inducing a given automorphism of $X$). | |
| Mar 23, 2015 at 9:13 | comment | added | naf | It seems to me that the "obvious guess" to your first question would be isomorphism classes of pairs $(Y,Z)$ so that $Y$ becomes isomorphic to $X$ and $Z$ becomes isomorphic to $\mathbb{P}^n$ over $\bar{k}$. For general line bunbdles this seems trickier... | |
| Mar 23, 2015 at 8:28 | history | edited | Daniel Loughran | CC BY-SA 3.0 |
deleted 9 characters in body
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| Mar 20, 2015 at 13:17 | comment | added | Daniel Loughran | I mean those $\sigma \in \mathrm{Aut} X$ such that $\sigma^*L \cong L$. Certainly I want $\mathrm{Aut}(\mathbb{P}^n, \mathcal{O}(1) )$ to be $\mathrm{PGL}_{n+1}$. | |
| Mar 20, 2015 at 12:31 | comment | added | Jason Starr | What precisely do you mean by "preserve the isomorphism class"? For instance, it seems to me that $\text{Aut}(\mathbb{P}^n_k,\mathcal{O}(1))$ is $\textbf{PGL}_{n+1}$. There is a slightly different notion that recovers $\textbf{SL}_{n+1}$. Some of this is discussed in my paper with de Jong, "Discriminant avoidance ..." | |
| Mar 20, 2015 at 10:30 | history | asked | Daniel Loughran | CC BY-SA 3.0 |