Derived Category of certain maximal order on ℙ²

2024/09/30 by Yu Shen, Shen, Yu
Mathematics · #14J60 #16H05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2409.19857

openalex publication_date 2024/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the moduli space of A-line bundles with minimal second Chern class is a fine moduli space, where A is a maximal quaternion order on ℙ² ramified along a smooth quartic. We prove that there is a fully faithful embedding from the derived category of this moduli space into the derived category of A-modules. Furthermore, we find a semiorthogonal decomposition for D^b(ℙ²,A).

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