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This article is cited in 1 scientific paper (total in 1 paper)
Uniform Lower Bound for Intersection Numbers of $\psi$-Classes
Vincent Delecroixa, Élise Goujardb, Peter Zografcd, Anton Zorichef a LaBRI, Domaine universitaire, 351 cours de la Libération, 33405 Talence, France
b Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 cours de la Libération, 33405 Talence, France
c Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
d Chebyshev Laboratory, St. Petersburg State University,
14th Line V.O. 29B, St. Petersburg, 199178, Russia
e Center for Advanced Studies, Skoltech, Russia
f Institut de Mathématiques de Jussieu – Paris Rive Gauche, Bâtiment Sophie Germain, Case 7012, 8 Place Aurélie Nemours, 75205 PARIS Cedex 13, France
Abstract:
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 approximating
expressions multiplied by an explicit factor $\lambda(g,n)$, which tends to $1$ when $g\to\infty$ and
$d_1+\dots+d_{n-2}=o(g)$.
Keywords:
intersection numbers, $\psi$-classes, Witten–Kontsevich correlators, moduli space of curves, large genus asymptotics.
Received: April 9, 2020; in final form August 21, 2020; Published online August 26, 2020
Citation:
Vincent Delecroix, Élise Goujard, Peter Zograf, Anton Zorich, “Uniform Lower Bound for Intersection Numbers of $\psi$-Classes”, SIGMA, 16 (2020), 086, 13 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1623 https://www.mathnet.ru/eng/sigma/v16/p86
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