• Corpus ID: 220380932

Curve counting and S-duality

  title={Curve counting and S-duality},
  author={Soheyla Feyzbakhsh and Richard P. Thomas},
  journal={arXiv: Algebraic Geometry},
We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker conjecture of Bayer-Macri-Toda, such as $\mathbb P^3$ or the quintic threefold. We prove certain moduli spaces of 2-dimensional torsion sheaves on $X$ are smooth bundles over Hilbert schemes of ideal sheaves of curves and points in $X$. When $X$ is Calabi-Yau this gives a simple wall crossing formula expressing curve counts (and so ultimately Gromov-Witten invariants) in terms of counts of D4-D2-D0 branes. These… 

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