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 |
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| Дата: | 2020 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862570358209511424 |
|---|---|
| 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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| first_indexed | 2026-03-13T11:52:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210762 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T11:52:35Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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. en 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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