Let $G$ be a group of automorphisms acting on a curve $X/\C$ of genus at least $2$, let $g_0$ be the genus of the quotient $Y:=X/G$, let $B$ be the set of branch points of the projection $\phi\colon X\to Y$, and let $m_1 \leq m_2 \leq \ldots \leq m_r$ be the orders of the standard generators for $\pi_1(Y-B,y_0)$ corresponding to the elements of $B=\{y_1,\ldots,y_r\}$.

The sequence of integers $[g_0; m_1, \ldots, m_r]$ is the **signature** of the group action.

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**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2018-06-29 20:50:17

**Referred to by:**

- curve.highergenus.aut.dimension
- dq.curve.highergenus.aut.label
- dq.curve.highergenus.aut.source
- lmfdb/higher_genus_w_automorphisms/main.py (line 1048)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-search.html (line 19)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-show-family.html (line 22)
- lmfdb/higher_genus_w_automorphisms/templates/hgcwa-show-passport.html (line 17)

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