The Coleman–Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of generically contained in the Jacobian locus. Counterexamples are known for ≤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, or c) ≤9. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for ≤100 there are no other families than those already known.
Some evidence for the Coleman–Oort conjecture
Conti, D;
2022-01-01
Abstract
The Coleman–Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of generically contained in the Jacobian locus. Counterexamples are known for ≤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, or c) ≤9. By means of carefully designed computations and theoretical arguments excluding a large number of cases we are able to prove that for ≤100 there are no other families than those already known.File in questo prodotto:
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