Abstract

We describe the Chow ring with rational coefficients of the moduli space of stable maps with marked points _0,m(ℙⁿ, d) as the subring of invariants of a ring B*( _0,m(ℙⁿ, d); ℚ), relative to the action of the group of symmetries S_d. B*( _0,m(ℙⁿ, d); ℚ) is computed by following a sequence of intermediate spaces for _0,m(ℙⁿ, d) and relating them to substrata of _0,1(ℙⁿ, d + m - 1). An additive basis for A*( _0,m(ℙⁿ, d); ℚ) is given.