Uniform Lower Bound for Intersection Numbers of -Classes

We approximate intersection numbers ⟨ᵈ¹₁⋯ ᵈⁿₙ⟩,ₙ on Deligne-Mumford's moduli space M¯,ₙ of genus stable complex curves with n marked points by certain closed-form expressions in d₁, …, dₙ. Conjecturally, these approximations become asymptotically exact uniformly in ᵢ when → ∞ and n remain bou...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2020
Автори: Delecroix, Vincent, Goujard, Élise, Zograf, Peter, Zorich, Anton
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2020
Онлайн доступ: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
Цитувати:Uniform Lower Bound for Intersection Numbers of -Classes. Vincent Delecroix, Élise Goujard, Peter Zograf and Anton Zorich. SIGMA 16 (2020), 086, 13 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Delecroix, Vincent
Goujard, Élise
Zograf, Peter
Zorich, Anton
author_facet Delecroix, Vincent
Goujard, Élise
Zograf, Peter
Zorich, Anton
citation_txt Uniform Lower Bound for Intersection Numbers of -Classes. Vincent Delecroix, Élise Goujard, Peter Zograf and Anton Zorich. SIGMA 16 (2020), 086, 13 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We approximate intersection numbers ⟨ᵈ¹₁⋯ ᵈⁿₙ⟩,ₙ on Deligne-Mumford's moduli space M¯,ₙ of genus stable complex curves with n marked points by certain closed-form expressions in d₁, …, dₙ. Conjecturally, these approximations become asymptotically exact uniformly in ᵢ when → ∞ 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(, ), which tends to 1 when → ∞ and d₁ +⋯+ dₙ₋₂ = o().
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spelling Delecroix, Vincent
Goujard, Élise
Zograf, Peter
Zorich, Anton
2025-12-17T14:30:04Z
2020
Uniform Lower Bound for Intersection Numbers of -Classes. Vincent Delecroix, Élise Goujard, Peter Zograf and Anton Zorich. SIGMA 16 (2020), 086, 13 pages
1815-0659
2020 Mathematics Subject Classification: 14C17; 14H70
arXiv:2004.02749
https://nasplib.isofts.kiev.ua/handle/123456789/210762
https://doi.org/10.3842/SIGMA.2020.086
We approximate intersection numbers ⟨ᵈ¹₁⋯ ᵈⁿₙ⟩,ₙ on Deligne-Mumford's moduli space M¯,ₙ of genus stable complex curves with n marked points by certain closed-form expressions in d₁, …, dₙ. Conjecturally, these approximations become asymptotically exact uniformly in ᵢ when → ∞ 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(, ), which tends to 1 when → ∞ and d₁ +⋯+ dₙ₋₂ = o().
We thank A. Aggarwal for the precious comments on the preliminary version of this text, which allowed us to correct several misprints and improve the presentation. We are grateful to N. Anantharaman, A. Borodin, D. Chen, M. Kazarian, S. Lando, M. Moller, A. Okounkov, and M. Shapiro for stimulating discussions. We thank MPIM in Bonn and MSRI in Berkeley for providing us with an excellent working environment. We thank anonymous referees for their generous reports and for helpful suggestions that allowed us to improve the presentation. The research of the second author was partially supported by PEPS. The results of Section 1 were obtained at Saint Petersburg State University under the support of the RSF grant 19-71-30002. This material is based upon work supported by the ANR-19-CE40-0021 grant. It was also supported by the NSF Grant DMS-1440140 while some of the authors were in residence at the MSRI during the Fall 2019 semester.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Uniform Lower Bound for Intersection Numbers of -Classes
Article
published earlier
spellingShingle Uniform Lower Bound for Intersection Numbers of -Classes
Delecroix, Vincent
Goujard, Élise
Zograf, Peter
Zorich, Anton
title Uniform Lower Bound for Intersection Numbers of -Classes
title_full Uniform Lower Bound for Intersection Numbers of -Classes
title_fullStr Uniform Lower Bound for Intersection Numbers of -Classes
title_full_unstemmed Uniform Lower Bound for Intersection Numbers of -Classes
title_short Uniform Lower Bound for Intersection Numbers of -Classes
title_sort uniform lower bound for intersection numbers of -classes
url https://nasplib.isofts.kiev.ua/handle/123456789/210762
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