Geodesic
Categorical absorptions of singularities and degenerations
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)

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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 $\mathcal{X}$.
DOI : 10.46298/epiga.2024.10836
Classification : 14D06, 14E15, 14F08, 14J45 
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     title = {Categorical absorptions of singularities and degenerations},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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     year = {2023},
     doi = {10.46298/epiga.2024.10836},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2024.10836/}
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Kuznetsov, Alexander; Shinder, Evgeny. Categorical absorptions of singularities and degenerations. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2024.10836

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