Coleman's finiteness conjecture for curves with special-type Jacobians

Let gg be a sufficiently large genus, and let a smooth projective curve of genus gg have a Jacobian of ST type, as in the source. Coleman's conjecture. Only finitely many smooth projective curves of genus gg have Jacobians of ST type. This is presented alongside Oort's proposed generalization concerning special subvarieties of the Torelli locus; the source does not state whether Coleman's conjecture has been resolved.

Sources & referencesView supporting material

Primary source

Michael D. Fried, “Hurwitz space components; and the Coleman-Oort Conjecture”, arXiv:2509.08904 (2025).

Additional references

5 papers in this index state this conjecture (2007–2025). The statement above is taken from the most recent of them; the others are arXiv:1804.00228, arXiv:1703.03140, arXiv:1112.0933, arXiv:0711.2195.

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