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| Main Authors: | , |
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| Format: | Preprint |
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2019
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| Online Access: | https://arxiv.org/abs/1908.10296 |
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| _version_ | 1866914969616908288 |
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| author | Joshi, Kirti Pauly, Christian |
| author_facet | Joshi, Kirti Pauly, Christian |
| contents | In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius instability strata with opers (more precisely as opers of type $1$ in the terminology of the present paper) and related them to certain Quot-schemes of Frobenius direct images of line bundles. The main aim of this paper is to describe for any integer $q \geq 1$ a conjectural generalization of this correspondence between opers of type $q$ (which we introduce here) and Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also give a conjectural formula for the dimension of the Frobenius instability locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_10296 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Opers of higher types, Quot-schemes and Frobenius instability loci Joshi, Kirti Pauly, Christian Algebraic Geometry In this paper we continue our study of the Frobenius instability locus in the coarse moduli space of semi-stable vector bundles of rank $r$ and degree $0$ over a smooth projective curve defined over an algebraically closed field of characteristic $p>0$. In a previous paper we identified the "maximal" Frobenius instability strata with opers (more precisely as opers of type $1$ in the terminology of the present paper) and related them to certain Quot-schemes of Frobenius direct images of line bundles. The main aim of this paper is to describe for any integer $q \geq 1$ a conjectural generalization of this correspondence between opers of type $q$ (which we introduce here) and Quot-schemes of Frobenius direct images of vector bundles of rank $q$. We also give a conjectural formula for the dimension of the Frobenius instability locus. |
| title | Opers of higher types, Quot-schemes and Frobenius instability loci |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/1908.10296 |