Higher rank DT/PT wall-crossing in Bridgeland stability

Fuente: arXiv
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Main Authors: Jardim, Marcos, Lo, Jason, Maciocia, Antony, Martinez, Cristian
Format: Preprint
Published: 2025
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author Jardim, Marcos
Lo, Jason
Maciocia, Antony
Martinez, Cristian
author_facet Jardim, Marcos
Lo, Jason
Maciocia, Antony
Martinez, Cristian
contents 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 $α>α_0$.
format Preprint
id arxiv_https___arxiv_org_abs_2503_20008
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Higher rank DT/PT wall-crossing in Bridgeland stability
Jardim, Marcos
Lo, Jason
Maciocia, Antony
Martinez, Cristian
Algebraic Geometry
14F05, 14J30
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 $α>α_0$.
title Higher rank DT/PT wall-crossing in Bridgeland stability
topic Algebraic Geometry
14F05, 14J30
url https://arxiv.org/abs/2503.20008