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Nondeformability of the complex projective space. (English) Zbl 0671.32018
A proof for the following conjecture of Kodaira and Spencer is given: Let \(\Delta\) be the open unit disk in \({\mathbb{C}}\) and let \(\pi\) : \(M\to \Delta\) be a holomorphic family of compact complex manifolds such that \(\pi^{- 1}(t)\) is biholomorphic to \({\mathbb{P}}_ n\) for \(t\in \Delta -0\). Then \(\pi^{-1}(0)\) is biholomorphic to \({\mathbb{P}}_ n\).
Reviewer: Y.-T.Siu

MSC:
32G07 Deformations of special (e.g., CR) structures
32J99 Compact analytic spaces
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