Some recent results in complex manifold theory related to vanishing theorems for the semipositive case. (English) Zbl 0577.32032

Arbeitstag. Bonn 1984, Proc. Meet. Max-Planck-Inst. Math., Bonn 1984, Lect. Notes Math. 1111, 169-192 (1985).
[For the entire collection see Zbl 0547.00007.]
This paper is a survey on vanishing theorems in complex analytic geometry.
The following three topics are discussed: (i) The construction of holomorphic sections for line bundles with semipositive curvature form; (ii) The strong rigidity of compact Kähler manifolds with seminegative curvature; (iii) Subelliptic estimates and their applications to vanishing theorems.
Reviewer: A.Pankov


32L20 Vanishing theorems
32Q99 Complex manifolds
32J99 Compact analytic spaces
53C55 Global differential geometry of Hermitian and Kählerian manifolds


Zbl 0547.00007