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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.11874 |
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| _version_ | 1866912829508943872 |
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| author | Pal, Sarbeswar |
| author_facet | Pal, Sarbeswar |
| contents | Let $C$ be a smooth irreducible irreducible projective curve of genus $g \ge 2$. Let $\mathcal{M}_C(n, δ)$ be the moduli space of semi-stable vector bundles on $C$ of rank $n$ and fixed determinant $δ$ of degree $d$. Then the locus of wobbly bundles is known to be closed in $\mathcal{M}_C(n, δ)$. It was announced by Laumon and attributed to Drinfeld that the wobbly locus is pure of co-dimension one, i.e., they form a divisor in $\mathcal{M}_C(n, δ)$. This is now known as Drinfeld's conjecture. In this article, we will give a proof of the conjecture when $n$ and $d$ are coprime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11874 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On a Conjecture of Drinfeld Pal, Sarbeswar Algebraic Geometry 14J60 Let $C$ be a smooth irreducible irreducible projective curve of genus $g \ge 2$. Let $\mathcal{M}_C(n, δ)$ be the moduli space of semi-stable vector bundles on $C$ of rank $n$ and fixed determinant $δ$ of degree $d$. Then the locus of wobbly bundles is known to be closed in $\mathcal{M}_C(n, δ)$. It was announced by Laumon and attributed to Drinfeld that the wobbly locus is pure of co-dimension one, i.e., they form a divisor in $\mathcal{M}_C(n, δ)$. This is now known as Drinfeld's conjecture. In this article, we will give a proof of the conjecture when $n$ and $d$ are coprime. |
| title | On a Conjecture of Drinfeld |
| topic | Algebraic Geometry 14J60 |
| url | https://arxiv.org/abs/2202.11874 |