2024/11/28 by Céline Fietz, Fietz, Céline
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2411.19380
openalex publication_date 2024/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a projective variety with an isolated A2 singularity. We study its bounded derived category and prove that there exists a crepant categorical resolution π_*\colon \widetildeD → Db(X), which is a Verdier localization. More importantly, we give an explicit description of a generating set for its kernel. In the case of an even dimensional variety with a single A2 singularity, we prove that this generating set is given by two 2-spherical objects. If X is a cubic fourfold with an isolated A2 singularity, we show that this resolution restricts to a crepant categorical resolution \widetildeAX of the Kuznetsov component AX ⊂ Db(X), which is equivalent to the bounded derived category of a K3 surface.