Timeline for Square root of relative Kähler differentials and families of curves
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8 at 20:05 | history | edited | LSpice | CC BY-SA 4.0 |
Kahler -> Kähler
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| Dec 8 at 19:47 | history | became hot network question | |||
| Dec 8 at 19:41 | vote | accept | Zhiyu | ||
| Dec 8 at 19:16 | comment | added | Piotr Achinger | Yes, $2^{2g}$ of course. | |
| Dec 8 at 16:08 | answer | added | Will Sawin | timeline score: 6 | |
| Dec 8 at 14:26 | comment | added | Jason Starr | As alluded by user @abx, these are classically known as "theta characteristics." They can be either "even" or "odd" depending on the parity of the dimension of the vector space of global sections. | |
| Dec 8 at 11:29 | comment | added | abx | @Piotr Achinger: double?? I would say of degree $2^{2g}$ (or $2^{g-1}(2^g\pm 1)$, to be more precise). | |
| Dec 8 at 8:01 | comment | added | Piotr Achinger | The "good locus" is a finite etale double cover (outside characteristic 2). | |
| Dec 8 at 5:12 | comment | added | abx | I don't think this has a simple answer. Take your example: $S$ a curve, $X=\mathbb{P}(E)$ with $E$ a rank 2 vector bundle; then $K_{X/S}$ has a square root if and only if $\deg E$ is even. | |
| Dec 8 at 2:03 | history | asked | Zhiyu | CC BY-SA 4.0 |