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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.00526 |
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| _version_ | 1866909234794332160 |
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| author | Leal, Manuel Huerta, Cesar Lozano Ryan, Tim |
| author_facet | Leal, Manuel Huerta, Cesar Lozano Ryan, Tim |
| contents | We show that the minimal free resolution of a general semi-stable sheaf $U$ on $\mathbb{P}^2$ contains a subcomplex that determines an extremal ray of the cone of effective divisors of its moduli space. We provide evidence that this is part of a general phenomenon in which minimal free resolutions, for distinct Betti tables, contain subcomplexes depending on wall-crossing. From this viewpoint, we provide new computations of the movable cones and Mori decompositions of some moduli spaces of sheaves using syzygies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometry of syzygies of sheaves on $\mathbb{P}^2$ via interpolation and Bridgeland stability Leal, Manuel Huerta, Cesar Lozano Ryan, Tim Algebraic Geometry We show that the minimal free resolution of a general semi-stable sheaf $U$ on $\mathbb{P}^2$ contains a subcomplex that determines an extremal ray of the cone of effective divisors of its moduli space. We provide evidence that this is part of a general phenomenon in which minimal free resolutions, for distinct Betti tables, contain subcomplexes depending on wall-crossing. From this viewpoint, we provide new computations of the movable cones and Mori decompositions of some moduli spaces of sheaves using syzygies. |
| title | Geometry of syzygies of sheaves on $\mathbb{P}^2$ via interpolation and Bridgeland stability |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.00526 |