Timeline for Why is a general curve automorphism-free?
Current License: CC BY-SA 2.5
7 events
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| Feb 11, 2011 at 15:24 | comment | added | Torsten Ekedahl | You are perfectly right. Another proof which works in all characteristics is to use that the representation of the automorphism group on points of order dividing $\ell$, a prime different from $p$ and at least $3$, is faithful. | |
| Feb 11, 2011 at 14:50 | comment | added | paul Monsky | There's one delicate point when the (algebraically closed) ground field is countable. The counting argument only shows that the set of curves of a fixed genus g>2 lies in a countable union of closed subsets of dimension <3g-3. So one also needs to bound the number of automorphisms independently of the curve. This is done using Weierstrass gaps; in characteristic p, the argument, which is a bit tricky, was carried out by H.L. Schmid in the 1930's. | |
| Feb 11, 2011 at 0:10 | vote | accept | jlk | ||
| Feb 10, 2011 at 10:48 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
Missed a term in the Hurwitz formula.
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| Feb 10, 2011 at 9:38 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
added 762 characters in body
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| Feb 10, 2011 at 9:13 | history | edited | Torsten Ekedahl | CC BY-SA 2.5 |
added 232 characters in body
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| Feb 10, 2011 at 7:47 | history | answered | Torsten Ekedahl | CC BY-SA 2.5 |