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).

17 pages, AMSLatex

References in corpus (1)

• Equivariant intersection theory

Cited by in corpus (5)

• Logarithmic series and Hodge integrals in the tautological ring (with an appendix by D. Zagier)
• The Chow Ring of the Hilbert Scheme of Rational Normal Curves
• An Additive Basis for the Chow Ring of \bar{M}_{0,2}(P^r,2)
• A presentation for the Chow ring A^*(\bar{M}_{0,2}(P^1,2))
• The Equivariant Chow Ring of SO(4)