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arXiv · 2311.09557

Products of boundary classes on M_0,n-bar via balanced weights

Maria Gillespie·Jake Levinson
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Abstract

In this note, we give a simple closed formula for an arbitrary product, landing in dimension 0, of boundary classes on the Deligne--Mumford moduli space M_0,n-bar. For any such boundary strata $X_{T_1}, \ldots, X_{T_\ell}$, we show the intersection product $\int \prod_{i=1}^\ell [X_{T_i}]$ is either a signed product of multinomial coefficients, or zero, and provide a simple criterion for determining when it is nonzero. We do not claim originality for our product formula, but to our knowledge it does not appear elsewhere in the literature.

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Maria Gillespie, Jake Levinson. 2023-11-16. Products of boundary classes on M_0,n-bar via balanced weights. https://arxiv.org/abs/2311.09557

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