Fay Identities of Pfaffian Type for Hyperelliptic Curves
We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212253 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fay Identities of Pfaffian Type for Hyperelliptic Curves. Gaëtan Borot and Thomas Buc-d'Alché. SIGMA 20 (2024), 054, 38 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862692696998543360 |
|---|---|
| author | Borot, Gaëtan Buc-d'Alché, Thomas |
| author_facet | Borot, Gaëtan Buc-d'Alché, Thomas |
| citation_txt | Fay Identities of Pfaffian Type for Hyperelliptic Curves. Gaëtan Borot and Thomas Buc-d'Alché. SIGMA 20 (2024), 054, 38 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form, we reprove them by direct geometric methods.
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| first_indexed | 2026-03-17T23:35:28Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212253 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T23:35:28Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Borot, Gaëtan Buc-d'Alché, Thomas 2026-02-03T07:54:43Z 2024 Fay Identities of Pfaffian Type for Hyperelliptic Curves. Gaëtan Borot and Thomas Buc-d'Alché. SIGMA 20 (2024), 054, 38 pages 1815-0659 2020 Mathematics Subject Classification: 60B20; 14H42 arXiv:2312.12229 https://nasplib.isofts.kiev.ua/handle/123456789/212253 https://doi.org/10.3842/SIGMA.2024.054 We establish identities of Pfaffian type for the theta function associated with twice or half the period matrix of a hyperelliptic curve. They are implied by the large size asymptotic analysis of exact Pfaffian identities for expectation values of ratios of characteristic polynomials in ensembles of orthogonal or quaternionic self-dual random matrices. We show that they amount to identities for the theta function with the period matrix of a hyperelliptic curve, and in this form, we reprove them by direct geometric methods. G.B. thanks Semyon Klevtsov for his encouragement to carry out this study, Angela Ortega for discussions on quadrisecants, and IHES (where this article was revised) for hospitality and excellent work conditions. T.B. is supported by the ERC Project LDRAM: ERC-2019-ADG Project 884584. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Fay Identities of Pfaffian Type for Hyperelliptic Curves Article published earlier |
| spellingShingle | Fay Identities of Pfaffian Type for Hyperelliptic Curves Borot, Gaëtan Buc-d'Alché, Thomas |
| title | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| title_full | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| title_fullStr | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| title_full_unstemmed | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| title_short | Fay Identities of Pfaffian Type for Hyperelliptic Curves |
| title_sort | fay identities of pfaffian type for hyperelliptic curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212253 |
| work_keys_str_mv | AT borotgaetan fayidentitiesofpfaffiantypeforhyperellipticcurves AT bucdalchethomas fayidentitiesofpfaffiantypeforhyperellipticcurves |