The irreducibility of the moduli space of pointed stable curves with dormant $\mathrm{PGL}_2^{(N)}$-oper
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914022007242752 |
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| author | Wakabayashi, Yasuhiro |
| author_facet | Wakabayashi, Yasuhiro |
| contents | A $\mathrm{PGL}_n^{(N)}$-oper is a specific type of flat $\mathrm{PGL}_n$-bundle on an algebraic curve in prime characteristic $p$ enhanced by an action of the sheaf of differential operators of level $N-1$. In this paper, we introduce and study a higher-level generalization of the Hitchin-Mochizuki morphism on the moduli space of $\mathrm{PGL}_n^{(N)}$-opers, defined via the characteristic polynomials of their $p^N$-curvatures. As an application, we prove the irreducibility of the moduli space classifying pointed stable curves equipped with dormant $\mathrm{PGL}_2^{(N)}$-opers, i.e., $\mathrm{PGL}_2^{(N)}$-opers with vanishing $p^N$-curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The irreducibility of the moduli space of pointed stable curves with dormant $\mathrm{PGL}_2^{(N)}$-oper Wakabayashi, Yasuhiro Algebraic Geometry A $\mathrm{PGL}_n^{(N)}$-oper is a specific type of flat $\mathrm{PGL}_n$-bundle on an algebraic curve in prime characteristic $p$ enhanced by an action of the sheaf of differential operators of level $N-1$. In this paper, we introduce and study a higher-level generalization of the Hitchin-Mochizuki morphism on the moduli space of $\mathrm{PGL}_n^{(N)}$-opers, defined via the characteristic polynomials of their $p^N$-curvatures. As an application, we prove the irreducibility of the moduli space classifying pointed stable curves equipped with dormant $\mathrm{PGL}_2^{(N)}$-opers, i.e., $\mathrm{PGL}_2^{(N)}$-opers with vanishing $p^N$-curvature. |
| title | The irreducibility of the moduli space of pointed stable curves with dormant $\mathrm{PGL}_2^{(N)}$-oper |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2509.03982 |