A Map Between Moduli Spaces of Connections
We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to lift such connections to an elliptic curve. The transformation...
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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/123456789/211094 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | A Map Between Moduli Spaces of Connections. Frank Loray and Valente Ramírez. SIGMA 16 (2020), 125, 42 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862707015682359296 |
|---|---|
| author | Loray, Frank Ramírez, Valente |
| author_facet | Loray, Frank Ramírez, Valente |
| citation_txt | A Map Between Moduli Spaces of Connections. Frank Loray and Valente Ramírez. SIGMA 16 (2020), 125, 42 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to lift such connections to an elliptic curve. The transformation is as follows: given an elliptic curve with elliptic quotient π: → ℙ¹, and the logarithmic connection (, ∇) on ℙ¹, we may pullback the connection to the elliptic curve to obtain a new connection (π*, π*∇) on . After suitable birational modifications, we bring the connection to a particular normal form. The whole transformation is equivariant with respect to bundle automorphisms and therefore defines a map between the corresponding moduli spaces of connections. This paper aims to describe the moduli spaces involved and compute explicit expressions for the above map in the case where the target space is the moduli space of rank 2 logarithmic connections on an elliptic curve with two simple poles and trivial determinant.
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| first_indexed | 2026-03-19T03:12:44Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211094 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T03:12:44Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Loray, Frank Ramírez, Valente 2025-12-23T13:14:01Z 2020 A Map Between Moduli Spaces of Connections. Frank Loray and Valente Ramírez. SIGMA 16 (2020), 125, 42 pages 1815-0659 2020 Mathematics Subject Classification: 14D20; 32G34; 34M55; 14H52; 53D30 arXiv:1910.13535 https://nasplib.isofts.kiev.ua/handle/123456789/211094 https://doi.org/10.3842/SIGMA.2020.125 We are interested in studying moduli spaces of rank 2 logarithmic connections on elliptic curves having two poles. To do so, we investigate certain logarithmic rank 2 connections defined on the Riemann sphere and a transformation rule to lift such connections to an elliptic curve. The transformation is as follows: given an elliptic curve with elliptic quotient π: → ℙ¹, and the logarithmic connection (, ∇) on ℙ¹, we may pullback the connection to the elliptic curve to obtain a new connection (π*, π*∇) on . After suitable birational modifications, we bring the connection to a particular normal form. The whole transformation is equivariant with respect to bundle automorphisms and therefore defines a map between the corresponding moduli spaces of connections. This paper aims to describe the moduli spaces involved and compute explicit expressions for the above map in the case where the target space is the moduli space of rank 2 logarithmic connections on an elliptic curve with two simple poles and trivial determinant. Most of the present work was carried out while the second author was a postdoc at IRMAR. He would like to thank the IRMAR and the Université de Rennes for hosting him during this period. We would like to thank Thiago Fassarella and Nestor Fernandez Vargas for many valuable discussions on this topic. We also thank Nicolas Tholozan, who helped us to understand the action of top on the symplectic 2-form on the monodromy side. Were also thankful to the anonymous referees for providing many suggestions to improve the content and clarity of the text. F.L. acknowledges the support of CNRS and the project Foliage ANR-16-CE40-0008. V.R. was supported by the grants PAPIIT IN-106217, CONACYT 219722, and the PRESTIGE postdoc program (coordinated by Campus France and co-financed under the Marie Curie ActionsCOFUND of the FP7). He also acknowledges the support of the Centre Henri Lebesgue ANR11-LABX-0020-01. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications A Map Between Moduli Spaces of Connections Article published earlier |
| spellingShingle | A Map Between Moduli Spaces of Connections Loray, Frank Ramírez, Valente |
| title | A Map Between Moduli Spaces of Connections |
| title_full | A Map Between Moduli Spaces of Connections |
| title_fullStr | A Map Between Moduli Spaces of Connections |
| title_full_unstemmed | A Map Between Moduli Spaces of Connections |
| title_short | A Map Between Moduli Spaces of Connections |
| title_sort | map between moduli spaces of connections |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211094 |
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