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

Ramadas, Rohini

doi:10.1090/proc/15486

Pullbacks of $\kappa$ classes on $\overline {\mathcal {M}}_{0,n}$
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Proc. Amer. Math. Soc. 149 (2021), 3245-3260 Request permission

Abstract:

The moduli space $\overline {\mathcal {M}}_{0,n}$ carries a codimension-$d$ Chow class $\kappa _{d}$. We consider the subspace $\mathcal {K}^{d}_{n}$ 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 $\mathcal {K}^{d}_{n}$, 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 $\overline {\mathcal {M}}_{0,n}$.

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