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In this talk, we will study the following question: how many degree d
curves are there in CP^2, that pass through d(d+3)/2-2 generic points and
have one cusp? While this question has been studied earlier by several different
approaches, in this talk, we will give a solution to this problem by extending
the degeneration idea of Caporaso and Harris (which so far has been used
to enumerate nodal curves).
If time permits, we will also talk about another generalization of the Caporaso-Harris, formula, namely a family version of their formula, which can be used to count curves in a moving family of surfaces. |