Uniform Lower Bound for Intersection Numbers of $\psi$-Classes
| Autor: | Vincent Delecroix, Peter Zograf, Elise Goujard, Anton Zorich |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Physics
010102 general mathematics Geometric topology Lambda 01 natural sciences Upper and lower bounds Moduli space Combinatorics Mathematics - Geometric Topology Intersection Genus (mathematics) Bounded function 0103 physical sciences 010307 mathematical physics Geometry and Topology 0101 mathematics Mathematical Physics Analysis |
| Zdroj: | Symmetry, Integrability and Geometry: Methods and Applications |
| Popis: | We approximate intersection numbers $\big\langle \psi_1^{d_1}\cdots \psi_n^{d_n}\big\rangle_{g,n}$ 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 $\lambda(g,n)$, which tends to $1$ when $g\to\infty$ and $d_1+\dots+d_{n-2}=o(g)$. Comment: Dedicated to D.B. Fuchs on the occasion of his 80th birthday |
| Databáze: | OpenAIRE |
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