The integral monodromy of hyperelliptic and trielliptic curves
By Jeff Achter, R. Pries. 2006
51 citations recorded by the source corpus.
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 $${\rm SU}_{(r,s)}(\mathbb{Z}/\ell\otimes\mathbb{Z}[\zeta_{3}])$$.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/31ad55ccfe8d4ec430f788a5ca5b281b1f504323
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Big symplectic or orthogonal monodromy modulo $\ell$ (2006, background): “See [Yu] for the preprint containing Yu’s original proof or [ AP ] for another recent independent proof.”
- Homological stability for Hurwitz spaces and the Cohen-Lenstra conjecture over function fields (2009, unknown): “In fact, Γ is the whole group Sp2g(Zl) when l is odd; this is due originally to unpublished work of Jiu-Kang Yu, and has been proved more recently in papers of Achter–Pries [3] and Hall [24].”
- Statistics for Traces of Cyclic Trigonal Curves over Finite Fields (2009, background): “We refer the reader to [1] for the details.”