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Rank $r$ DT theory from rank $0$

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 نشر من قبل R. P. Thomas
 تاريخ النشر 2021
  مجال البحث
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Fix a Calabi-Yau 3-fold $X$ satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr`i-Toda, such as the quintic 3-fold. We express Joyces generalised DT invariants counting Gieseker semistable sheaves of any rank $rge1$ on $X$ in terms of those counting sheaves of rank 0 and pure dimension 2. The basic technique is to reduce the ranks of sheaves by replacing them by the cokernels of their Mochizuki/Joyce-Song pairs and then use wall crossing to handle their stability.



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