An obstructed bundle on a Calabi-Yau 3-fold

Details An obstructed bundle on a Calabi-Yau 3-fold An obstructed bundle on a Calabi-Yau 3-fold

1999-03-05

arxiv.org/abs/math/9903034v1

Adv. Theor. Math. Phys. 3, 567-576, 1999.

Mathematics

Algebraic Geometry

Scientific paper

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.

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