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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автори: Borot, Gaëtan, Buc-d'Alché, Thomas
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/212253
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
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.
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