Moduli of non-pure sheaves and contractions of Hilbert schemes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918127091056640 |
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| author | Herrero, Andres Fernandez Makarova, Svetlana |
| author_facet | Herrero, Andres Fernandez Makarova, Svetlana |
| contents | We define certain stacks of rank one sheaves on a smooth projective variety, and show that they admit proper good moduli spaces. We offer several applications to contractions of subschemes inside Hilbert schemes of points. We construct a surgery diagram via non-GIT wall-crossing, and use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata's DK-hypothesis in this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Moduli of non-pure sheaves and contractions of Hilbert schemes Herrero, Andres Fernandez Makarova, Svetlana Algebraic Geometry 14D23 (Primary) 14D20, 14E05, 14F08 (Secondary) We define certain stacks of rank one sheaves on a smooth projective variety, and show that they admit proper good moduli spaces. We offer several applications to contractions of subschemes inside Hilbert schemes of points. We construct a surgery diagram via non-GIT wall-crossing, and use the interpretation of the surgery as a fine moduli of sheaves to prove instances Kawamata's DK-hypothesis in this setting. |
| title | Moduli of non-pure sheaves and contractions of Hilbert schemes |
| topic | Algebraic Geometry 14D23 (Primary) 14D20, 14E05, 14F08 (Secondary) |
| url | https://arxiv.org/abs/2508.13395 |