Orientation data on moduli space of sheaves on Calabi-Yau threefold
arXiv:1212.3790
Abstract
Kontsevich and Soibelman introduced a notion of orientation data on Calabi-Yau category. It can be viewed as a consistent choice of spin structure on moduli space of objects in the given category. The orientation data plays an important role in Donaldson-Thomas theory. Let X be a projective, simply connected and torsion free CY 3-fold. We prove the existence of orientation data for the moduli space of coherent sheaves on X.
The proof of the consistence contains a mistake that cannot be fixed