Timeline for Reference for hyperelliptic curves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12, 2015 at 15:30 | comment | added | rfauffar | Dear Noam: yes, this is a great way to see what is happening in general. | |
| Jan 10, 2015 at 21:45 | comment | added | Noam D. Elkies | $\ldots$, $\kappa$ is a $2:1$ map to a rational normal curve, and if $\lambda$ preserves that curve $\kappa(C)$ then it comes from a fractional linear transformation of ${\bf P}^1$, etc. | |
| Jan 10, 2015 at 21:45 | comment | added | Noam D. Elkies | More generally: A curve $C$ of genus $g>1$ has a canonical map $\kappa: C \rightarrow {\bf P}^{g-1}$. Since it's canonical, for any automorphism $\alpha: C \rightarrow C$ the composite map $\kappa \alpha: C \rightarrow {\bf P}^{g-1}$ must be the same as $\kappa$ up to some linear automorphism $\lambda$ of ${\bf P}^{g-1}$, so $\kappa\alpha = \lambda\kappa$. For example, the automorphisms of a plane quartic are exactly the linear automorphisms of the plane that preserve the quartic. In our hyperelliptic setting$\ldots$ [cont'd because of 600-character limit] | |
| Aug 16, 2013 at 1:54 | history | answered | rfauffar | CC BY-SA 3.0 |