Pullbacks of 𝜅 classes on \overline{ℳ}_{0,𝓃}

Abstract

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