Intersections of Q-Divisors on Kontsevich's Moduli Space M_0,n(P^r,d) and Enumerative Geometry

1995/04/06 by Rahul Pandharipande, R. Pandharipande, Pandharipande, R. · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9504004

AMSLaTex 31 pages

arxiv created 1995/04/06 · openalex publication_date 1995/04/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The theory of 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 Q-Divisors is established. As a corollary, an algorithm computing all characteristic numbers of rational curves in 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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• A presentation for the Chow ring A^*(M_0,2(P¹,2))

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