Some evidence for the Coleman–Oort conjecture

The Coleman–Oort conjecture says that for large g there are no positive-dimensional Shimura subvarieties of Ag A g generically contained in the Jacobian locus. Counterexamples are known for g≤ 7 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, or c) g≤ 9 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 g ≤ 100 there are no other families than those already known.