The integral Chow ring of M_{0}(P^r,d)

We give an efficient presentation of the Chow ring with integral coefficients of the open part of the moduli space of rational maps of odd degree to projective space. A less fancy description of this space has its closed points correspond to equivalence classes of $(r+1)$-tuples of degree $d$ polynomials in one variable with no common positive degree factor. We identify this space as a $GL(2,\mathbb{C})$ quotient of an open set in a projective space, and then obtain a (highly redundant) presentation by considering an envelope of the complement. A combinatorial analysis then leads us to eliminating a large number of relations, and to express the remaining ones in generating function form for all dimensions. The upshot of this work is to observe the rich combinatorial structure contained in the Chow rings of these moduli spaces as the degree and the target dimension vary. This is joint work with Damiano Fulghesu.