An obstructed bundle on a Calabi-Yau 3-fold

Abstract

Mirror symmetry suggests that on a Calabi-Yau 3-fold moduli spaces of stable bundles, especially those with degree zero and indivisible Chern class, might be smooth (i.e. unobstructed, though perhaps of too high a dimension). This is because smoothly embedded special lagrangian cycles in the mirror have unobstructed deformations. As there does not seem to be a counterexample in the literature we provide one here, showing that such a Tian-Todorov-McLean-type result cannot hold.