On the enumeration of rational plane curves with tangency conditions
نویسنده
چکیده
We use twisted stable maps to answer the following question. Let E ⊂ P2 be a smooth cubic. How many rational degree d curves pass through a general points of E , have b specified tangencies with E and c unspecified tangencies, and pass through 3d − 1 − a − 2b − c general points of P2? The answer is given as a generalization of Kontsevich’s recursion. We also investigate more general enumerative problems of this sort, and prove an analogue of a formula of Caporaso and Harris.
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