The integral Chow ring of ${\mathcal{M}}_0({\mathbb{P}}^r,2)$

Abstract

We compute a presentation for the integral Chow rings of the moduli stacks of degree $2$ maps from smooth rational curves to projective space ${\mathbb{P}}^r$, as a quotient of a three-variable polynomial ring. The relations as $r$ varies have rich combinatorial structure: all non-trivial relations are encoded by two generating functions which are rational functions.

14 pages