Categorical absorptions of singularities and degenerations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910258675318784 |
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| author | Kuznetsov, Alexander Shinder, Evgeny |
| author_facet | Kuznetsov, Alexander Shinder, Evgeny |
| contents | We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper category. We construct (under appropriate assumptions) a categorical absorption for a projective variety $X$ with isolated ordinary double points. We further show that for any smoothing $\mathcal{X}/B$ of $X$ over a smooth curve $B$, the smooth part of the derived category of $X$ extends to a smooth and proper over $B$ family of triangulated subcategories in the fibers of $\mathcal{X}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06477 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Categorical absorptions of singularities and degenerations Kuznetsov, Alexander Shinder, Evgeny Algebraic Geometry We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper category. We construct (under appropriate assumptions) a categorical absorption for a projective variety $X$ with isolated ordinary double points. We further show that for any smoothing $\mathcal{X}/B$ of $X$ over a smooth curve $B$, the smooth part of the derived category of $X$ extends to a smooth and proper over $B$ family of triangulated subcategories in the fibers of $\mathcal{X}$. |
| title | Categorical absorptions of singularities and degenerations |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2207.06477 |