Orientation data for moduli spaces of coherent sheaves over Calabi–Yau 3-folds

<p>Let X be a compact Calabi–Yau 3-fold, and write M,M for the moduli stacks of objects in coh(X), Dbcoh(X). There are natural line bundles KM → M, KM → M, analogues of canonical bundles. Orientation data on M,M is an isomorphism class of square root line bundles K1/2 M , K1/2 M , satisfying a...