Intersections of ℚ-divisors on Kontsevich’s moduli space \overline{𝕄}_{0,𝕟}(ℙ^{𝕣},𝕕) and enumerative geometry

Pandharipande, Rahul

doi:10.1090/S0002-9947-99-01909-1

Intersections of $\mathbb {Q}$-divisors on Kontsevich’s moduli space $\overline {M}_{0,n}(\mathbb {P}^r,d)$ and enumerative geometry
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by Rahul Pandharipande

Trans. Amer. Math. Soc. 351 (1999), 1481-1505

DOI: https://doi.org/10.1090/S0002-9947-99-01909-1

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Abstract:

The theory of $\mathbb Q$-Cartier divisors on the space of $n$-pointed, genus 0, stable maps to projective space is considered. Generators and Picard numbers are computed. A recursive algorithm computing all top intersection products of $\mathbb Q$-divisors is established. As a corollary, an algorithm computing all characteristic numbers of rational curves in $\mathbb P^r$ is proven (including simple tangency conditions). Computations of these characteristic numbers are carried out in many examples. The degree of the 1-cuspidal rational locus in the linear system of degree $d$ plane curves is explicitly evaluated.

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