2023/11/09 by Andrew Hanlon, Hanlon, Andrew, J. Hicks +1
Mathematics · Physics and Astronomy · #14F08 #18G80 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2311.05753
openalex publication_date 2023/11/09 · openalex created_date 2023/11/14 · openalex updated_date 2026/07/28
Given a dg category \mathcal C, we introduce a new class of objects (weakly product bimodules) in \mathcal Cop⊗ \mathcal C generalizing product bimodules. We show that the minimal generation time of the diagonal by weakly product bimodules provides an upper bound for the Rouquier dimension of \mathcal C. As an application, we give a purely algebro-geometric proof of a result of Burban and Drozd that the Rouquier dimension of the derived category of coherent sheaves on an n-cycle of projective lines is one. Our approach explicitly gives the generator realizing the minimal generation time.