Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Certainly, if we fix the genus $g$ of a curve $X$, we have $\# $Aut$(X) \leq 84(g-1)$.

Let $X$ be a hyperelliptic curve. Is there a bound on $\#$Aut$(X)$? (Note that I do not want to fix the genus!)

More generally, can $\#$Aut$(X)$ be bounded in terms of the gonality of $X$?

share|cite|improve this question
The answer is no even for gonality 2. Try to prove that. – user18119 Jan 31 '13 at 16:31
The curve $y^2=x^{2g+1}+1$ admits the automorphism $(x,y)\mapsto (\zeta_{2g+1}^n x, y)$ for all $n=1,\ldots,2g+1$. Thus, the number of automorphisms of this hyperelliptic curve is at least $2g+1$. Is this correct? – Harry Feb 2 '13 at 9:34
Yes in characteristic $0$. Otherwise consider $y^2=x^{p^n}-x$ in characteristic $p>2$. – user18119 Feb 2 '13 at 17:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.