The generic étaleness of the moduli space of dormant $\mathfrak{so}_{2\ell}$-opers
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929469641457664 |
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| author | Wakabayashi, Yasuhiro |
| author_facet | Wakabayashi, Yasuhiro |
| contents | The generic étaleness is an important property on the moduli space of dormant $\mathfrak{g}$-opers (for a simple Lie algebra $\mathfrak{g}$) in the context of enumerative geometry. In the previous study, this property has been verified under the assumption that $\mathfrak{g}$ is either $\mathfrak{sl}_\ell$, $\mathfrak{so}_{2\ell -1}$, or $\mathfrak{sp}_{2\ell}$ for any sufficiently small positive integer $\ell$. The purpose of the present paper is to prove the generic étaleness for one of the remaining cases, i.e., $\mathfrak{g} = \mathfrak{so}_{2\ell}$. As an application of this result, we obtain a factorization formula for computing the generic degree induced from pull-back along various clutching morphisms between moduli spaces of pointed stable curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12264 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The generic étaleness of the moduli space of dormant $\mathfrak{so}_{2\ell}$-opers Wakabayashi, Yasuhiro Algebraic Geometry The generic étaleness is an important property on the moduli space of dormant $\mathfrak{g}$-opers (for a simple Lie algebra $\mathfrak{g}$) in the context of enumerative geometry. In the previous study, this property has been verified under the assumption that $\mathfrak{g}$ is either $\mathfrak{sl}_\ell$, $\mathfrak{so}_{2\ell -1}$, or $\mathfrak{sp}_{2\ell}$ for any sufficiently small positive integer $\ell$. The purpose of the present paper is to prove the generic étaleness for one of the remaining cases, i.e., $\mathfrak{g} = \mathfrak{so}_{2\ell}$. As an application of this result, we obtain a factorization formula for computing the generic degree induced from pull-back along various clutching morphisms between moduli spaces of pointed stable curves. |
| title | The generic étaleness of the moduli space of dormant $\mathfrak{so}_{2\ell}$-opers |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2408.12264 |