Alexander Kuznetsov ; Evgeny Shinder - Categorical absorptions of singularities and degenerations

epiga:10836 - Épijournal de Géométrie Algébrique, January 9, 2024, Special volume in honour of Claire Voisin -
Categorical absorptions of singularities and degenerationsArticle

Authors: Alexander Kuznetsov ; Evgeny Shinder

    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 $\mathcal{X}$.

    Volume: Special volume in honour of Claire Voisin
    Published on: January 9, 2024
    Accepted on: September 25, 2023
    Submitted on: January 20, 2023
    Keywords: Mathematics - Algebraic Geometry

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