The Chow Ring of the Non-Linear Grassmannian

Abstract

Let M_{P^k}(P^r, d) be the moduli space of unparameterized maps μ:P^k -> P^r satisfying μ^*(O(1))= O(d). M_{P^k}(P^r,d) is a quasi-projective variety, and, in case k=1, M_{P^1}(P^r,d) is the fundamental open cell of Kontsevich's space of stable maps \bar{M}_{0,0}(P^r,d). It is shown that the Q-coefficient Chow ring of M_{P^k}(P^r,d) is canonically isomorphic to the Chow ring of the Grassmannian Gr(P^k, P^r)= M_{P^k}(P^r,1).