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An obstructed bundle on a Calabi-Yau 3-fold
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.Comment: Corrected mistake pointed out by Yukinobu Tod
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