ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 32, 58 Wu, Siye, Department of Pure Mathematics, University of Adelaide, Adelaide, SA 5005, Australia On the instanton complex of holomorphic Morse theory Consider holomorphic group actions on vector bundles over complex manifolds. Under the Kähler assumption, Morse-type inequalities were obtained by Witten and proved analytically by Mathai, Zhang and myself. These inequalities could fail without the Kähler condition. In this talk, I construct the holomorphic analog of instanton complex when there is a partial ordering on the set of connected components of the fixed-point set; this assumption is much weaker than the Kähler condition. Furthermore, the construction completely determines Dolbeault cohomology groups by the combinatorial data of the group action.