The integral monodromy of hyperelliptic and trielliptic curves

Details The integral monodromy of hyperelliptic and trielliptic curves The integral monodromy of hyperelliptic and trielliptic curves

2006-08-01

arxiv.org/abs/math/0608038v2

Mathematics

Algebraic Geometry

Scientific paper

We compute the $\integ/\ell$ and $\integ_\ell$ monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we provide a proof that the $\integ/\ell$ monodromy of the moduli space of hyperelliptic curves of genus $g$ is the symplectic group $\sp_{2g}(\integ/\ell)$. We prove that the $\integ/\ell$ monodromy of the moduli space of trielliptic curves with signature $(r,s)$ is the special unitary group $\su_{(r,s)}(\integ/\ell\tensor\integ[\zeta_3])$.

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