most recent 30 from http://mathoverflow.net 2013-05-19T20:15:56Z http://mathoverflow.net/feeds/question/109243 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/109243/genus-two-curve-with-special-automorphisms xuehang 2012-10-09T17:37:11Z 2012-10-09T18:18:58Z

<p>Is it possible to find a genus two curve $C$ (over the field of complex numbers) with an endomorphism $\phi: C \to C$, such that $\phi$ has no fixed points and $\phi$ does not take any point to its hyperelliptic involution?</p>

http://mathoverflow.net/questions/109243/genus-two-curve-with-special-automorphisms/109246#109246 Felipe Voloch 2012-10-09T18:18:58Z 2012-10-09T18:18:58Z

<p>No, $\phi$ must come from an automorphism of $\mathbb{P}^1$ and that has fixed points.</p>