1998/06/22 by Siye Wu, Wu, Siye
Mathematics · #14F05 (Primary) 32C35 #32M05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F05 #msc:32C35 #msc:32M05
paper · pdf · doi:10.48550/arxiv.math/9806118
plain LaTeX, 30 pages
arxiv created 1998/06/22 · arxiv updated 2009/11/30
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.