All Questions

I am in an ideal situation but I would appreciate a hint. First here is the scenario. Let $\mathcal{J}$ be an the abelian variety obtained from the Jacobian of a genus $2$ curve $\mathcal{H}/k$ ...

I wonder if the following is known: Are there two compact curves C1 and C2 of genus>1 defined over complex numbers, such that their product contains infinite number of irreducible curves of negative ...