Holomorphic Morse inequalities. (English) Zbl 0755.32008

Several complex variables and complex geometry, Proc. Summer Res. Inst., Santa Cruz/CA (USA) 1989, Proc. Symp. Pure Math. 52, Part 2, 93-114 (1991).
[For the entire collection see Zbl 0732.00008.]
In this paper the complex analogues of the Morse inequalities for \(\overline\partial\)-cohomology groups with values in holomorphic vector bundles are explained, and some applications of that theory are presented.
Reviewer: B.Nowak (Łódź)


32C35 Analytic sheaves and cohomology groups
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
32L10 Sheaves and cohomology of sections of holomorphic vector bundles, general results
53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)


Zbl 0732.00008