Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation
We introduce the notion of factorized ramified structure on a generic ramified irregular singular connection on a smooth projective curve. By using the deformation theory of connections with factorized ramified structure, we construct a canonical 2-form on the moduli space of ramified connections. S...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2023 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2023
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211871 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation. Michi-aki Inaba. SIGMA 19 (2023), 013, 72 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862648720115367936 |
|---|---|
| author | Inaba, Michi-aki |
| author_facet | Inaba, Michi-aki |
| citation_txt | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation. Michi-aki Inaba. SIGMA 19 (2023), 013, 72 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We introduce the notion of factorized ramified structure on a generic ramified irregular singular connection on a smooth projective curve. By using the deformation theory of connections with factorized ramified structure, we construct a canonical 2-form on the moduli space of ramified connections. Since the factorized ramified structure provides a duality on the tangent space of the moduli space, the 2-form becomes nondegenerate. We prove that the 2-form on the moduli space of ramified connections is d-closed via constructing an unfolding of the moduli space. Based on the Stokes data, we introduce the notion of local generalized isomonodromic deformation for generic unramified irregular singular connections on a unit disk. Applying the Jimbo-Miwa-Ueno theory to generic unramified connections, the local generalized isomonodromic deformationis equivalent to the extendability of the family of connections to an integrable connection. We give the same statement for ramified connections. Based on this principle of Jimbo-Miwa-Ueno theory, we construct a global generalized isomonodromic deformation on the moduli space of generic ramified connections by constructing a horizontal lift of a universal family of connections. As a consequence of the global generalized isomonodromic deformation, we can lift the relative symplectic form on the moduli space to a total closed form, which is called a generalized isomonodromic 2-form.
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| first_indexed | 2026-03-15T13:34:19Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211871 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T13:34:19Z |
| publishDate | 2023 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Inaba, Michi-aki 2026-01-14T09:54:15Z 2023 Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation. Michi-aki Inaba. SIGMA 19 (2023), 013, 72 pages 1815-0659 2020 Mathematics Subject Classification: 14D20; 53D30; 34M56; 34M40 arXiv:2108.09667 https://nasplib.isofts.kiev.ua/handle/123456789/211871 https://doi.org/10.3842/SIGMA.2023.013 We introduce the notion of factorized ramified structure on a generic ramified irregular singular connection on a smooth projective curve. By using the deformation theory of connections with factorized ramified structure, we construct a canonical 2-form on the moduli space of ramified connections. Since the factorized ramified structure provides a duality on the tangent space of the moduli space, the 2-form becomes nondegenerate. We prove that the 2-form on the moduli space of ramified connections is d-closed via constructing an unfolding of the moduli space. Based on the Stokes data, we introduce the notion of local generalized isomonodromic deformation for generic unramified irregular singular connections on a unit disk. Applying the Jimbo-Miwa-Ueno theory to generic unramified connections, the local generalized isomonodromic deformationis equivalent to the extendability of the family of connections to an integrable connection. We give the same statement for ramified connections. Based on this principle of Jimbo-Miwa-Ueno theory, we construct a global generalized isomonodromic deformation on the moduli space of generic ramified connections by constructing a horizontal lift of a universal family of connections. As a consequence of the global generalized isomonodromic deformation, we can lift the relative symplectic form on the moduli space to a total closed form, which is called a generalized isomonodromic 2-form. The author would like to thank Professor Takuro Mochizuki for having a discussion and giving useful advice. The author would also like to thank Professor Arata Komyo for having useful discussions frequently. The author would like to thank the referee for valuable comments to improve the paper. This work is partially supported by JSPS Grant-in-Aid for Scientific Research (C) 19K03422. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation Article published earlier |
| spellingShingle | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation Inaba, Michi-aki |
| title | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation |
| title_full | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation |
| title_fullStr | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation |
| title_full_unstemmed | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation |
| title_short | Moduli Space of Factorized Ramified Connections and Generalized Isomonodromic Deformation |
| title_sort | moduli space of factorized ramified connections and generalized isomonodromic deformation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211871 |
| work_keys_str_mv | AT inabamichiaki modulispaceoffactorizedramifiedconnectionsandgeneralizedisomonodromicdeformation |