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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Curves with negative self intersection in the product of two curvesI 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 curve.
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