Communications in Number Theory and Physics
Volume 10 (2016)
Vertical sheaves and Fourier–Mukai transform on elliptic Calabi–Yau threefolds
Pages: 373 – 431
This paper studies the action of the Fourier–Mukai transform on moduli spaces of vertical torsion sheaves on elliptic Calabi–Yau threefolds in Weierstrass form. Moduli stacks of semistable one dimensional sheaves on such threefolds are identified with open and closed substacks of moduli stacks of vertical semistable two dimensional sheaves on their Fourier–Mukai duals. In particular, this yields explicit conjectural results for Donaldson–Thomas invariants of vertical two dimensional sheaves on K3-fibered elliptic Calabi–Yau threefolds.