Nondeformability of the complex projective space. (English) Zbl 0671.32018

Siu, Yum-Tong

J. Reine Angew. Math. 399, 208-219 (1989).

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