Papers › Some evidence for the Coleman-Oort conjecture
Some evidence for the Coleman-Oort conjecture
Diego Conti, Alessandro Ghigi, Roberto Pignatelli
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The Coleman-Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of 𝖠_g generically contained in the Jacobian locus. Counterexamples are known for g≤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≤9. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for g≤100 there are no other families than those already known.
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