Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 085, 16 pages      math.AG/0501322      https://doi.org/10.3842/SIGMA.2007.085

An Additive Basis for the Chow Ring of M0,2(Pr,2)

Jonathan A. Cox
Department of Mathematical Sciences, SUNY Fredonia, Fredonia, New York 14063, USA

Received July 03, 2007, in final form August 28, 2007; Published online August 31, 2007

Abstract
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.

Key words: moduli space of stable maps; Chow ring; Betti numbers.

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