Let K be an algebraically closed field of characteristic p>0, and let X be an algebraic curve over K of genus g>1. Assume that p>2 and that X admits a non-singular plane model. The following result is proven: if X has more than 3(2g^2+g)(3+(8g+1)^(1/2)) automorphisms, then X is birationally equivalent to a Hermitian curve.
On the size of the automorphism group of a plane algebraic curve
BARTOLI, DANIELE;GIULIETTI, Massimo
2013
Abstract
Let K be an algebraically closed field of characteristic p>0, and let X be an algebraic curve over K of genus g>1. Assume that p>2 and that X admits a non-singular plane model. The following result is proven: if X has more than 3(2g^2+g)(3+(8g+1)^(1/2)) automorphisms, then X is birationally equivalent to a Hermitian curve.File in questo prodotto:
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