CATEGORICAL SINGULARITIES DEGENERATIONS

. 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 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 X .

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