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

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.

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

References in corpus (6)

• Relations between the correlators of the topological sigma-model coupled to gravity
• Mixed Hodge structures of configuration spaces
• On the cohomology of stable map spaces
• The tautological rings of the moduli spaces of stable maps
• The Chow Ring of the Non-Linear Grassmannian
• Tautological classes on the moduli spaces of stable maps to projective spaces

Cited by in corpus (1)

• A presentation for the Chow ring A^*(\bar{M}_{0,2}(P^1,2))