Curves of given p-rank with trivial automorphism group

Jeffrey D. Achter, Darren Glass, Rachel Pries
2008 The Michigan mathematical journal  
Let k be an algebraically closed field of characteristic p > 0. Suppose g ≥ 3 and 0 ≤ f ≤ g. We prove there is a smooth projective k-curve of genus g and p-rank f with no non-trivial automorphisms. In addition, we prove there is a smooth projective hyperelliptic k-curve of genus g and p-rank f whose only non-trivial automorphism is the hyperelliptic involution. The proof involves computations about the dimension of the moduli space of (hyperelliptic) k-curves of genus g and p-rank f with extra
more » ... -rank f with extra automorphisms. 2000 Mathematics Subject Classification. 11G20, 14H05.
doi:10.1307/mmj/1231770361 fatcat:pztouwzdsjcaxe22hgytok44za