Plurisubharmonically separable complex manifolds

T"-Aetions on Holomorphically Separable Complex Manifolds*

Here we consider complex manifolds M which are holomorphically separable, i.e., the global holomorphic functions (9 (M) separate the points of M. We investigate T n (n-torus) actions on M, where T"={(ei~ ei~ 0eN"}, and n is the complex dimension of M. We assume that the action is effective, i.e., if 0ET ~ is nonzero, then there exists z e M with O.z+z. Our final assumption on the action is one ...

Non-separable Hilbert Manifolds of Continuous Mappings

Using Toruńczyk’s charaterization theorem, we show that the space CB(X,Y ) of bounded continuous mappings from X into Y is a topological manifold modelled on the Hilbert space of weight 20 , with respect to the topology of uniform convergence, under the following three assumptions: (1) X is a noncompact, separable and metrizable space, (2) Y is a complete metric space which is an ANRU (ANR in u...

Complex Manifolds

is holomorphic. Thus P has the structure of a complex manifold, called complex projective space. The “coordinates” Z + [Z0, . . . , Zn] are called homogeneous coordinates on P. P is compact, since we have a continuous surjective map from the unit sphere in C to P. Note that P is just the Riemann sphere C ∪ {∞}. Any inclusion C → C induces an inclusion P → P; the image of such a map is called a ...

COMPLEX b-MANIFOLDS

A complex b-structure on a manifold M with boundary is an involutive subbundle bT 0,1M of the complexification of bTM with the property that CbTM = bT 0,1M + bT 0,1M as a direct sum; the interior of M is a complex manifold. The complex b-structure determines an elliptic complex of b-operators and induces a rich structure on the boundary of M. We study the cohomology of the indicial complex of t...

Complex Parallisable Manifolds