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An Additive Basis for the Chow Ring of $\overline{\mathcal M}_{0,2}(\mathbb P^r,2)$
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: moduli space of stable maps; Chow ring; Betti numbers. 
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     title = {An {Additive} {Basis} for the {Chow} {Ring} of $\overline{\mathcal M}_{0,2}(\mathbb P^r,2)$},
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Jonathan A. Cox. An Additive Basis for the Chow Ring of $\overline{\mathcal M}_{0,2}(\mathbb P^r,2)$. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a84/

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