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A natural basis for intersection numbers
Eynard, Bertrand
Lewański, Danilo
2023
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e-ISSN
2464-8728
Abstract
We advertise elementary symmetric polynomials ei as the natural basis for generating series Ag,n of intersection numbers of ψ-classes on the moduli space of stable curves of genus g with n marked
points. Closed formulae for Ag,n are known for genera 0 and 1 — this approach provides formulae for g = 2, 3, 4, together with an algorithm to compute the formula for any g.
The claimed naturality of the ei basis relies in the unexpected vanishing of some coefficients with a clear pattern. As an application of the conjecture, we find new integral representations of Ag,n, which recover expressions for the Weil-Petersson volumes in terms of Bessel functions.
Source
Bertrand Eynard, Danili Lewański, "A natural basis for intersection numbers" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.55 (2023)", EUT Edizioni Università di Trieste, Trieste, 2023, pp. 117-163
Languages
en
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