  We work on a projective threefold $X$ which satisfies the Bogomolov-Gieseker
conjecture of Bayer-Macr\`i-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 latter invariants are predicted to have modular
properties which we discuss from the point of view of S-duality and
Noether-Lefschetz theory.
