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Rank r DT theory from rank 1

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If you have a question about this talk, please contact Dhruv Ranganathan.

Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macr\`i-Toda, such as the quintic 3-fold. After a brief introduction of weak Bridgeland stability conditions, I will describe work with Richard Thomas which expresses Joyce’s generalised DT invariants counting Gieseker semistable sheaves of any rank r on X in terms of those counting sheaves of rank 1. By the MNOP conjecture, the latter are determined by the Gromov-Witten invariants of X. Finally, I will show our result gives an explicit formula for rank r=0 or 2 when X is of Picard rank one.

This talk is part of the Algebraic Geometry Seminar series.

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