Fattening complex manifolds: Curvature and Kodaira—Spencer maps

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Abstract

We present a calculus whereby the curvature of a geometry arising from any generalized twistor correspondence is related to an obstruction-theoretic classification of the infinitesimal neighborhoods of submanifolds of its twistor space. The crux of the argument involves a relation between Kodaira—Spencer maps and the Penrose transform.

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∗

Supported in part by the Australian Research Council.

∗∗

Supported in part by the NSF and by the Australian Research Council.

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Copyright © 1992 Published by Elsevier B.V.