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arXiv · 2102.12349

Some evidence for the Coleman-Oort conjecture

Diego Conti·Alessandro Ghigi·Roberto Pignatelli
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Abstract

The Coleman-Oort conjecture says that for large $g$ there are no positive-dimensional Shimura subvarieties of $\mathsf{A}_g$ generically contained in the Jacobian locus. Counterexamples are known for $g\leq 7$. They can all be constructed using families of Galois coverings of curves satisfying a numerical condition. These families are already classified in cases where: a) the Galois group is cyclic, b) it is abelian and the family is 1-dimensional, and c) $g\leq 9$. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for $g\leq 100$ there are no other families than those already known.

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Diego Conti, Alessandro Ghigi, Roberto Pignatelli. 2021-02-24. Some evidence for the Coleman-Oort conjecture. https://doi.org/10.1007/s13398-021-01195-0

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