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Higher rank DT/PT wall-crossing in Bridgeland stability https://arxiv.org/abs/2503.20008 #mathAG

Higher rank DT/PT wall-crossing in Bridgeland stability

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 $α>α_0$.

arXiv.org
March 28, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 0
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