On the Instanton Complex of Holomorphic Morse Theory

Details On the Instanton Complex of Holomorphic Morse Theory On the Instanton Complex of Holomorphic Morse Theory

1998-06-22

arxiv.org/abs/math/9806118v1

Mathematics

Algebraic Geometry

plain LaTeX, 30 pages

Scientific paper

Consider a holomorphic torus action on vector bundles over a complex manifold which lifts to a holomorphic vector bundle. When the connected components of the fixed-point set are partially ordered, we construct, using sheaf-theoretical techniques, two spectral sequences that converges to the twisted Dolbeault cohomology groups and those with compact support, respectively. These spectral sequences are the holomorphic counterparts of the instanton complex in standard Morse theory. The results proved imply holomorphic Morse inequalities and fixed-point formulas on a possibly non-compact manifold. Finally, a number of examples and applications are given.

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