The integral monodromy of hyperelliptic and trielliptic curves期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The integral monodromy of hyperelliptic and trielliptic curves

Authors:	Jeffrey D Achter Rachel Pries

Institution:	(1) Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA

Abstract:	We compute the $\mathbb{Z}/\ell$ and $\mathbb{Z}_{\ell}$ monodromy of every irreducible component of the moduli spaces of hyperelliptic and trielliptic curves. In particular, we provide a proof that the $\mathbb{Z}/\ell$ monodromy of the moduli space of hyperelliptic curves of genus g is the symplectic group ${\rm S}_{P2g}(\mathbb{Z}/\ell)$ . We prove that the $\mathbb{Z}/\ell$ monodromy of the moduli space of trielliptic curves with signature (r,s) is the special unitary group ${\rm SU}_{(r,s)}(\mathbb{Z}/\ell\otimes\mathbb{Z}\zeta_{3}])$ . Rachel Pries was partially supported by NSF grant DMS-04-00461.

Keywords:	11G18 14D05 14H40
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