论文标题
$ψ$ - 类的交点的均匀下限
Uniform Lower Bound for Intersection Numbers of $ψ$-Classes
论文作者
论文摘要
我们近似交点数$ \ big \langleψ_1^{d_1} \cdotsψ_n^{d_n} \ big big \ rangle_ {g，n} $ in Deligne-Mumford的moduli space $ \ overline $ \ overline {\ mathcal m} $ cultes $ nline $ $ d_1，\ dots，d_n $中的闭合形式表达式。猜想的是，当$ g \ to \ infty $和$ n $保持界限或生长缓慢时，这些近似在$ d_i $中渐近地均匀地均匀。在本说明中，我们证明了与上述近似表达式乘以显式因子$λ（g，n）$的近似值的下限，当$ g \ to \ g \ to \ hytty $和$ d_1+\ d_1+\ d_+d_+d_ {n-2} = o（g）$时，它往往$ 1 $。
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 $d_1+\dots+d_{n-2}=o(g)$.
