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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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

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.
References
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Additional Information
  • Rahul Pandharipande
  • Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
  • Address at time of publication: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
  • MR Author ID: 357813
  • Email: rahulp@cco.caltech.edu
  • Received by editor(s): March 11, 1996
  • Additional Notes: Partially supported by an NSF Post-Doctoral Fellowship.
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 1481-1505
  • MSC (1991): Primary 14N10, 14H10; Secondary 14E99
  • DOI: https://doi.org/10.1090/S0002-9947-99-01909-1
  • MathSciNet review: 1407707