On the enumeration of rational plane curves with tangency conditions

2005/09/28 by Charles Cadman, Cadman, Charles
Mathematics · #14N10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0509671

17 pages

arxiv created 2005/09/28 · arxiv updated 2009/12/01

Abstract

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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