Rank $r$ DT theory from rank $1$

Richard P. Thomas; Soheyla Feyzbakhsh

Rank $r$ DT theory from rank $1$

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arxiv 2108.02828 v2 pith:FSV6VFFX submitted 2021-08-05 math.AG hep-thmath.SG

Soheyla Feyzbakhsh , Richard P. Thomas This is my paper · ORCID

classification math.AGhep-thmath.SG

keywords rankconjecturecountingfoldinvariantssheavesbayer-macrbogomolov-gieseker

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abstract

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 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 they are therefore determined by the Gromov-Witten invariants of $X$.

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