2022/07/13 by Alexander Kuznetsov, Evgeny Shinder · 2 citations
Mathematics · Physics and Astronomy · #math.AG
paper · pdf · doi:10.46298/epiga.2024.10836
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.