Equivariant Holomorphic Morse Inequalities III: NonIsolated 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 fixedpoint set is not necessarily discrete. Such inequalities bound the twisted Dolbeault cohomologies of the Kahler manifold in terms of those of the fixedpoint set. We apply the inequalities to obtain relations of Hodge numbers of the connected components of the fixedpoint set and the whole manifold. We also investigate the consequences in geometric quantization, especially in the context of symplectic cutting.
 Publication:

eprint arXiv:dgga/9701009
 Pub Date:
 January 1997
 DOI:
 10.48550/arXiv.dgga/9701009
 arXiv:
 arXiv:dgga/9701009
 Bibcode:
 1997dg.ga.....1009W
 Keywords:

 Mathematics  Differential Geometry;
 53C55;
 58F05
 EPrint:
 plain LaTeX, 22 pages