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Given a group of automorphisms $G$ acting on a curve $X/\C$ of genus $g$, with signature $[g_0;m_1, \ldots, m_r]$, the dimension of the family of curves with this signature is $3g_0+r-3$, where $r$ is the number of branch points of the map $X \to X/G$ and $g_0$ is the quotient genus.

Knowl status:
  • Review status: reviewed
  • Last edited by Jennifer Paulhus on 2021-04-30 11:26:22
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