An Additive Basis for the Chow Ring of \bar{M}_{0,2}(P^r,2)

Details An Additive Basis for the Chow Ring of \bar{M}_{0,2}(P^r,2) An Additive Basis for the Chow Ring of \bar{M}_{0,2}(P^r,2)

2005-01-20

arxiv.org/abs/math/0501322v3

SIGMA 3 (2007), 085, 16 pages

Mathematics

Algebraic Geometry

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2007.085

We begin a study of the intersection theory of the moduli spaces of degree two stable maps from two-pointed rational curves to arbitrary-dimensional projective space. First we compute the Betti numbers of these spaces using Serre polynomial and equivariant Serre polynomial methods developed by E. Getzler and R. Pandharipande. Then, via the excision sequence, we compute an additive basis for their Chow rings in terms of Chow rings of nonlinear Grassmannians, which have been described by Pandharipande. The ring structure of one of these Chow rings is addressed in a sequel to this paper.

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