Curves of given $p$-rank with trivial automorphism group

Jeff Achter; Darren Glass; Rachel Pries

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arXiv · 0708.2199

Curves of given $p$-rank with trivial automorphism group

Jeff Achter·Darren Glass·Rachel Pries

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Abstract

Let $k$ be an algebraically closed field of characteristic $p >0$. Suppose $g \geq 3$ and $0 \leq f \leq g$. 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 automorphisms.

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BibTeX RIS

Jeff Achter, Darren Glass, Rachel Pries. 2007-08-16. Curves of given $p$-rank with trivial automorphism group. https://arxiv.org/abs/0708.2199

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