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, or 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.
Some evidence for the Coleman–Oort conjecture
Ghigi A.;
2022-01-01
Abstract
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, or 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
