For k>1, the noncompact Calabi-Yau threefold W_k admits infinitely many pairwise non-isomorphic complex deformations, and some of these deformations preserve nontrivial moduli spaces of rank-2 vector bundles.
Moduli stacks of bundles on local surfaces
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Infinite dimensional families of Calabi-Yau threefolds and moduli of vector bundles
For k>1, the noncompact Calabi-Yau threefold W_k admits infinitely many pairwise non-isomorphic complex deformations, and some of these deformations preserve nontrivial moduli spaces of rank-2 vector bundles.