Timeline for Embedding of symmetric square in Jacobian
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2023 at 9:51 | vote | accept | kindasorta | ||
| Sep 11, 2023 at 16:35 | answer | added | David E Speyer | timeline score: 3 | |
| Sep 11, 2023 at 16:34 | review | Close votes | |||
| Sep 17, 2023 at 3:05 | |||||
| Sep 11, 2023 at 16:34 | comment | added | kindasorta | As far as injectivity goes, the exercise should be something like: assume there is an effective degree 2 divisir $P+Q$ on $C$, and another one $R+S$, which are linearly equivalent, then there is a non-trivial degree 2 automorphism of $C$? | |
| Sep 11, 2023 at 16:32 | comment | added | kindasorta | First off: many thanks. I am away from my computer, if it is not too much of a burden could you find the reference in Arbarello et al? | |
| Sep 11, 2023 at 16:11 | comment | added | abx | Any book on curves — e.g. Arbarello et al. But at least for the injectivity, work it out by yourself, it follows directly from the definitions. | |
| Sep 11, 2023 at 15:59 | comment | added | kindasorta | Why is it the case? Do you have any references? | |
| Sep 11, 2023 at 15:52 | comment | added | abx | It is not an embedding if and only if $C$ admits a linear series of degree 2 and dimension $>0$, that is, if and only if $C$ is hyperelliptic. | |
| Sep 11, 2023 at 15:14 | history | asked | kindasorta | CC BY-SA 4.0 |