Pullbacks of $\kappa$ classes on ${\overline{\mathcal{M}}}_{0,n}$

Abstract

The moduli space ${\overline{\mathcal{M}}}_{0,n}$ carries a codimension-$d$ cycle class ${\kappa }_d$. We consider the subspace ${\mathcal{K}}_n^d$ of $A^d({\overline{\mathcal{M}}}_{0,n},\mathbb{Q})$ spanned by pullbacks of ${\kappa }_d$ via forgetful maps. We find a permutation basis for ${\mathcal{K}}_n^d$, and describe its annihilator under the intersection pairing in terms of $d$-dimensional boundary strata. As an application, we give a new permutation basis of the divisor class group of ${\overline{\mathcal{M}}}_{0,n}$.

11 pages; comments welcome