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arXiv 2004.027492020-04math.GT

Uniform Lower Bound for Intersection Numbers of $ψ$-Classes

Vincent Delecroix, Élise Goujard, Peter Zograf, Anton Zorich

备注：: Dedicated to D.B. Fuchs on the occasion of his 80th birthday
发表信息：: SIGMA 16 (2020), 086, 13 pages
DOI：: 10.3842/SIGMA.2020.086

英文摘要：

We approximate intersection numbers $\big\langle ψ_1^{d_1}\cdots ψ_n^{d_n}\big\rangle_{g,n}$ on Deligne-Mumford's moduli space $\overline{\mathcal M}_{g,n}$ of genus $g$ stable complex curves with $n$ marked points by certain closed-form expressions in $d_1,\dots,d_n$. Conjecturally, these approximations become asymptotically exact uniformly in $d_i$ when $g\to\infty$ and $n$ remains bounded or grows slowly. In this note we prove a lower bound for the intersection numbers in terms of the above-mentioned approximatingexpressions multiplied by an explicit factor $λ(g,n)$, which tends to $1$ when $g\to\infty$ and $d_1+\dots+d_{n-2}=o(g)$.

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