Higher rank DT/PT wall-crossing in Bridgeland stability

2025/03/25 by Marcos Jardim, Jardim, Marcos, Jason Lo +5 · 1 citation
Engineering · #14F05 #14J30 #Algebraic Geometry (math.AG) #Elevator Systems and Control #FOS: Mathematics #Geotechnical Engineering and Underground Structures #Structural Response to Dynamic Loads

paper · pdf · doi:10.48550/arxiv.2503.20008

openalex publication_date 2025/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Gieseker moduli space of stable sheaves on a smooth projective threefold X of Picard rank 1 is separated from the moduli space of PT stable objects by a single wall in the space of Bridgeland stability conditions on X, thus realizing the higher rank DT/PT correspondence as a wall-crossing phenomenon in the space of Bridgeland stability conditions. In addition, we also show that only finitely many walls pass through the upper (β,α)-plane parametrizing geometric Bridgeland stability conditions on X which destabilize Gieseker stable sheaves, PT stable objects or their duals when α>α₀.

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