The moduli space of dormant opers on elliptic curves
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908346826620928 |
|---|---|
| author | Karube, Naoka Wakabayashi, Yasuhiro |
| author_facet | Karube, Naoka Wakabayashi, Yasuhiro |
| contents | A dormant oper is a specific type of principal bundle with a flat connection, defined on an algebraic curve in positive characteristic. The moduli spaces of dormant opers and their variants, known as dormant Miura opers, have been studied in various contexts. This paper focuses on the case where the underlying spaces are (possibly nodal) elliptic curves and provides a detailed examination of the geometric structures of their moduli spaces. In particular, we explicitly describe dormant (generic Miura) opers in terms of regular elements in an associated Lie algebra and establish the connectedness of these moduli spaces. We also explore generalizations to higher level and prime-power characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The moduli space of dormant opers on elliptic curves Karube, Naoka Wakabayashi, Yasuhiro Algebraic Geometry A dormant oper is a specific type of principal bundle with a flat connection, defined on an algebraic curve in positive characteristic. The moduli spaces of dormant opers and their variants, known as dormant Miura opers, have been studied in various contexts. This paper focuses on the case where the underlying spaces are (possibly nodal) elliptic curves and provides a detailed examination of the geometric structures of their moduli spaces. In particular, we explicitly describe dormant (generic Miura) opers in terms of regular elements in an associated Lie algebra and establish the connectedness of these moduli spaces. We also explore generalizations to higher level and prime-power characteristic. |
| title | The moduli space of dormant opers on elliptic curves |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.00418 |