Announcement_2025 09 30

Our preprint Mumford-type Shimura curves contained in the Torelli locus is now on arXiv. We present two Shimura curves of Mumford type contained in the Torelli locus, one whose universal family is a hyperelliptic curve, and the other non-hyperelliptic, both of genus 4. The Jacobians of these curves are the first explicit examples of abelian varieties of the type described by Mumford in his article A Note of Shimura’s paper “Discontinuous Groups and Abelian Varieties”.

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You can find related code in our GitHub repo. In particular, the file Shimura_models.m contains equations for the universal curves of genus 4 mentioned above.