Serre functor and ℙ-objects for perverse sheaves on ℙⁿ

2025/06/06 by Lukas Bonfert, Bonfert, Lukas, Alessio Cipriani +1
Mathematics · #14F08 #16E35 #18G80 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2506.06051

openalex publication_date 2025/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the inverse Serre functor for the constructible derived category D^b_c(ℙⁿ) is given by the ℙ-twist at the simple perverse sheaf corresponding to the open stratum. Moreover, we show that all indecomposable perverse sheaves on ℙⁿ are ℙ-like objects, and explicitly construct morphisms spanning their total endomorphism spaces.

Citations

• On uniqueness of P-twists
• Flops and about: a guide
• Stability conditions, torsion theories and tilting
• TQFT with corners and tilting functors in the Kac-Moody case
• Tilting exercises
• Braid group actions on derived categories of coherent sheaves

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