Higher rank DT/PT wall-crossing in Bridgeland stability
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909552385982464 |
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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 |