# zbMATH — the first resource for mathematics

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
##### Keywords:
complex projective space; nondeformability
Full Text: