Some evidence for the Coleman-Oort conjecture

Authors :: Conti, Diego
Ghigi, Alessandro
Pignatelli, Roberto
Source :: Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM 116 (2022), no. 1, Paper No. 50
Publication Year :: 2021
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.<br />Comment: Accepted for publication on Revista de la Real Academia de Ciencias Exactas, F\'isicas y Naturales. Serie A. Matem\'aticas

Database :: arXiv
Journal :: Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A Mat. RACSAM 116 (2022), no. 1, Paper No. 50
Publication Type :: Report
Accession number :: edsarx.2102.12349
Document Type :: Working Paper
Full Text :: https://doi.org/10.1007/s13398-021-01195-0