Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914022028214272 |
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| author | Mori, Keita Wakabayashi, Yasuhiro |
| author_facet | Mori, Keita Wakabayashi, Yasuhiro |
| contents | This note studies $\mathrm{PGL}_n$-opers arising from generalized hypergeometric differential equations in prime characteristic $p$. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the $2$d TQFTs that compute the number of dormant $\mathrm{PGL}_n$-opers for primes $p \leq 7$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_03994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$ Mori, Keita Wakabayashi, Yasuhiro Algebraic Geometry This note studies $\mathrm{PGL}_n$-opers arising from generalized hypergeometric differential equations in prime characteristic $p$. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the $2$d TQFTs that compute the number of dormant $\mathrm{PGL}_n$-opers for primes $p \leq 7$. |
| title | Generalized hypergeometric equations and $2$d TQFT for dormant opers in characteristic $\leq 7$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.03994 |