On Frobenius' Theta Formula
Mumford's well-known characterization of the hyperelliptic locus of the moduli space of ppavs in terms of vanishing and non-vanishing theta constants is based on Neumann's dynamical system. Poor's approach to the characterization uses the cross ratio. A key tool in both methods is Fro...
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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/123456789/210693 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On Frobenius' Theta Formula. Alessio Fiorentino and Riccardo Salvati Manni. SIGMA 16 (2020), 057, 14 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | Mumford's well-known characterization of the hyperelliptic locus of the moduli space of ppavs in terms of vanishing and non-vanishing theta constants is based on Neumann's dynamical system. Poor's approach to the characterization uses the cross ratio. A key tool in both methods is Frobenius' theta formula, which follows from Riemann's theta formula. In a 2004 paper, Grushevsky gives a different characterization in terms of cubic equations in second-order theta functions. In this note, we first show the connection between the methods by proving that Grushevsky's cubic equations are strictly related to Frobenius' theta formula, and we then give a new proof of Mumford's characterization via Gunning's multisecant formula.
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| ISSN: | 1815-0659 |