Uniform Lower Bound for Intersection Numbers of 𝜓-Classes
We approximate intersection numbers ⟨𝜓ᵈ¹₁⋯ 𝜓ᵈⁿₙ⟩𝑔,ₙ on Deligne-Mumford's moduli space M¯𝑔,ₙ of genus 𝑔 stable complex curves with n marked points by certain closed-form expressions in d₁, …, dₙ. Conjecturally, these approximations become asymptotically exact uniformly in 𝑑ᵢ when 𝑔 → ∞ and n rem...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2020 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2020
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210762 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Uniform Lower Bound for Intersection Numbers of 𝜓-Classes. Vincent Delecroix, Élise Goujard, Peter Zograf and Anton Zorich. SIGMA 16 (2020), 086, 13 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We approximate intersection numbers ⟨𝜓ᵈ¹₁⋯ 𝜓ᵈⁿₙ⟩𝑔,ₙ on Deligne-Mumford's moduli space M¯𝑔,ₙ of genus 𝑔 stable complex curves with n marked points by certain closed-form expressions in d₁, …, dₙ. Conjecturally, these approximations become asymptotically exact uniformly in 𝑑ᵢ when 𝑔 → ∞ and n remain bounded or grow 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 λ(𝑔, 𝑛), which tends to 1 when 𝑔 → ∞ and d₁ +⋯+ dₙ₋₂ = o(𝑔).
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| ISSN: | 1815-0659 |