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Versal deformations and superpotentials for rational curves in smooth threefolds

Sheldon Katz
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Abstract

The versal deformation space of a smooth rational curve in a smooth complex threefold is explicitly computed under certain hypotheses. Under an additional hypothesis, the versal deformation space is then shown to be the variety of critical points of a holomorphic function, the superpotential, as predicted by the consideration of D-branes in string theory.

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Sheldon Katz. 2000-10-30. Versal deformations and superpotentials for rational curves in smooth threefolds. https://arxiv.org/abs/math/0010289

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