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arXiv · 2007.01338

Algebraic curves with automorphism groups of large prime order

Nazar Arakelian·Pietro Speziali
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Abstract

Let $\mathcal{X}$ be an algebraic curve of genus $g$ defined over an algebraically closed field $K$ of characteristic $p \geq 0$, and $q$ a prime dividing $|\mbox{Aut}(\mathcal{X})|$. We say that $\mathcal{X}$ is a $q$-curve. Homma proved that either $q \leq g+1$ or $q = 2g+1$, and classified $(2g+1)$-curves. In this note, we classify $(g+1)$-curves, and fully characterize the automorphism groups of $q$-curves for $q= 2g+1, g+1$. We also give some partial results on $q$-curves for $q = g, g-1$.

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Nazar Arakelian, Pietro Speziali. 2020-07-02. Algebraic curves with automorphism groups of large prime order. https://arxiv.org/abs/2007.01338

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