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| Format: | Preprint |
| Veröffentlicht: |
2021
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2112.14452 |
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| _version_ | 1866913554584567808 |
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| author | Kawamata, Yujiro |
| author_facet | Kawamata, Yujiro |
| contents | We investigate the behavior of semi-orthogonal decompositions of bounded derived categories of singular varieties under flat deformations to smooth varieties. We consider a Q-Gorenstein smoothing of a surface with a quotient singularity, and prove that a pretilting sheaf, which is constructed from a non-commutative deformation of a divisorial sheaf and generates a semi-orthogonal component of a bounded derived category, deforms to a direct sum of exceptional vector bundles which are mutually totally orthogonal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_14452 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Semi-orthogonal decomposition and smoothing Kawamata, Yujiro Algebraic Geometry 14J60, 14B07, 14E30 We investigate the behavior of semi-orthogonal decompositions of bounded derived categories of singular varieties under flat deformations to smooth varieties. We consider a Q-Gorenstein smoothing of a surface with a quotient singularity, and prove that a pretilting sheaf, which is constructed from a non-commutative deformation of a divisorial sheaf and generates a semi-orthogonal component of a bounded derived category, deforms to a direct sum of exceptional vector bundles which are mutually totally orthogonal. |
| title | Semi-orthogonal decomposition and smoothing |
| topic | Algebraic Geometry 14J60, 14B07, 14E30 |
| url | https://arxiv.org/abs/2112.14452 |