Timeline for Families of Hurwitz curves
Current License: CC BY-SA 3.0
3 events
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| May 24, 2013 at 17:10 | comment | added | Ariyan Javanpeykar | Here's an addendum to Will's answer to your question that might interest you. For any integer $g>1$, there are only finitely many curves $X$ of genus $g$ such that $X/ $ Aut$(X)$ is the projective line and the quotient map $X\to X/ $ Aut$(X)$ is ramified over only three points. (Same argument as Will's.) Such curves are called Galois Belyi curves, or Wolfart curves. Hurwitz curves are examples of Wolfart curves, but so are Fermat curves, and certain congruence modular curves. Anyway, the point I wanted to make is that such curves also cannot be put into a nontrivial family. | |
| May 24, 2013 at 15:47 | comment | added | Dhruv | Ah of course. The case that gives you the bound is when $X/G$ has genus zero. Should've seen that. Thank you! | |
| May 24, 2013 at 15:25 | history | answered | Will Sawin | CC BY-SA 3.0 |