Hecke curves in Frobenius strata of moduli space of rank 2 vector bundles
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908826197819392 |
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| author | Li, Lingguang Zhang, Hongyi |
| author_facet | Li, Lingguang Zhang, Hongyi |
| contents | Let $k$ be an algebraically closed field with characteristic $2$, and let $X$ be a smooth projective algebraic curve of genus $g \geqslant 2$ over $k$. Let $\mathcal{M}^s_X(2,\mathcal{L})$ be the moduli space of rank $2$ stable vector bundles with determinant $\mathcal{L}$ on $X$. The Frobenius stratification measures the instability of bundles in $\mathcal{M}^s_X(r,\mathcal{L})$ under pullback by the Frobenius map. We show that there exists a Frobenius stratum in $\mathcal{M}^s_X(2,\mathcal{L})$ which is covered by Hecke curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hecke curves in Frobenius strata of moduli space of rank 2 vector bundles Li, Lingguang Zhang, Hongyi Algebraic Geometry 14H60, 14G17, 14H45 Let $k$ be an algebraically closed field with characteristic $2$, and let $X$ be a smooth projective algebraic curve of genus $g \geqslant 2$ over $k$. Let $\mathcal{M}^s_X(2,\mathcal{L})$ be the moduli space of rank $2$ stable vector bundles with determinant $\mathcal{L}$ on $X$. The Frobenius stratification measures the instability of bundles in $\mathcal{M}^s_X(r,\mathcal{L})$ under pullback by the Frobenius map. We show that there exists a Frobenius stratum in $\mathcal{M}^s_X(2,\mathcal{L})$ which is covered by Hecke curves. |
| title | Hecke curves in Frobenius strata of moduli space of rank 2 vector bundles |
| topic | Algebraic Geometry 14H60, 14G17, 14H45 |
| url | https://arxiv.org/abs/2602.09879 |