Timeline for Kodaira dimension of symmetric products of curves
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 26, 2018 at 20:15 | history | edited | Francois Ziegler | CC BY-SA 4.0 |
typo
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| Jun 26, 2018 at 15:44 | history | edited | ACL | CC BY-SA 4.0 |
Corrected the Kodaira dimension of $C^{(d)}$ for $d>g$, as pointed out by pbelmans.
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| Jun 25, 2018 at 12:27 | comment | added | pbelmans | It's probably worth noting that $\kappa(C^{(d)})=-\infty$ for $d>g$, not 0: these symmetric powers are uniruled. One has $\kappa(C^{(g)})=0$ though, being birational to an abelian variety. | |
| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 8, 2013 at 13:59 | vote | accept | ACL | ||
| Mar 8, 2013 at 13:44 | answer | added | Olivier Benoist | timeline score: 25 | |
| Mar 8, 2013 at 7:58 | comment | added | M P | If the Jacobian of the curve is simple, then all its proper subvarieties are of general type; in particular the symmetric product of the curve is of general type, until the Abel-Jacobi map is surjective. By deformation, I would guess that the same is true for all curves, not just the ones that have simple Jacobian. | |
| Mar 8, 2013 at 7:33 | history | asked | ACL | CC BY-SA 3.0 |