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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 self-intersection and arbitrary large genus? It we aks the same question replacing "negative" by "zero", the answer will be yes, moreover there will be examples of with C1 and C2 of any genus. These examples can be obtained as ramified covers ExE where E is an elliptic curve.

(PS. The answers given to this question in 2009 did not solve it)

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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 self-intersection and arbitrary large genus? It we aks the same question replacing "negative" by "zero", the answer will be yes, moreover there will be a lot of examples of with C1 and C2 of any genus. These examples can be obtained as ramified covers ExE where E is an elliptic curve.

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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 curves of negative self-intersection? It we aks the same question replacing "negative" by "zero", the answer will be yes, moreover there will be a lot of examples of any genus. These examples can be obtained as ramified covers ExE where E is an ellitic elliptic curve.

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