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Parameter spaces for curves on surfaces and enumeration of rational curves

Lucia Caporaso·Joe Harris
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Abstract

We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's formula for rational plane curves of given degree.

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Lucia Caporaso, Joe Harris. 1996-08-22. Parameter spaces for curves on surfaces and enumeration of rational curves. https://arxiv.org/abs/alg-geom/9608024

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