Equivariant Holomorphic Morse Inequalities III: Non-Isolated Fixed Points
Abstract
We prove the equivariant holomorphic Morse inequalities for a holomorphic torus action on a holomorphic vector bundle over a compact Kahler manifold when the fixed-point set is not necessarily discrete. Such inequalities bound the twisted Dolbeault cohomologies of the Kahler manifold in terms of those of the fixed-point set. We apply the inequalities to obtain relations of Hodge numbers of the connected components of the fixed-point set and the whole manifold. We also investigate the consequences in geometric quantization, especially in the context of symplectic cutting.
- Publication:
-
eprint arXiv:dg-ga/9701009
- Pub Date:
- January 1997
- DOI:
- 10.48550/arXiv.dg-ga/9701009
- arXiv:
- arXiv:dg-ga/9701009
- Bibcode:
- 1997dg.ga.....1009W
- Keywords:
-
- Mathematics - Differential Geometry;
- 53C55;
- 58F05
- E-Print:
- plain LaTeX, 22 pages