On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics
A parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M4m ± 1(ℙ2)...
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-02-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2018-0003 |
| _version_ | 1819122022025789440 |
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| author | Iena Oleksandr |
| author_facet | Iena Oleksandr |
| author_sort | Iena Oleksandr |
| collection | DOAJ |
| description | A parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M4m ± 1(ℙ2) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. Two different proofs of this statement are given. |
| first_indexed | 2024-12-22T06:45:50Z |
| format | Article |
| id | doaj.art-18f99e7106f545ec8ba8c604943b80cf |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-22T06:45:50Z |
| publishDate | 2018-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-18f99e7106f545ec8ba8c604943b80cf2022-12-21T18:35:17ZengDe GruyterOpen Mathematics2391-54552018-02-01161466210.1515/math-2018-0003math-2018-0003On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quarticsIena Oleksandr0Luxembourg, USAA parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M4m ± 1(ℙ2) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. Two different proofs of this statement are given.https://doi.org/10.1515/math-2018-0003simpson moduli spaces1-dimensional sheavesblow-upblow-downquotients by non-reductive groups14d20 |
| spellingShingle | Iena Oleksandr On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics Open Mathematics simpson moduli spaces 1-dimensional sheaves blow-up blow-down quotients by non-reductive groups 14d20 |
| title | On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics |
| title_full | On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics |
| title_fullStr | On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics |
| title_full_unstemmed | On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics |
| title_short | On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics |
| title_sort | on the fine simpson moduli spaces of 1 dimensional sheaves supported on plane quartics |
| topic | simpson moduli spaces 1-dimensional sheaves blow-up blow-down quotients by non-reductive groups 14d20 |
| url | https://doi.org/10.1515/math-2018-0003 |
| work_keys_str_mv | AT ienaoleksandr onthefinesimpsonmodulispacesof1dimensionalsheavessupportedonplanequartics |