Deformations of complex analytic subspaces with locally stable parametrizations of compact complex manifolds

Associative deformations of complex analytic spaces

A theory of associative deformations is developed for general complex analytic spaces. Deformation quantization and commutative deformation are particular cases of this concept. Deformation cohomology and obstruction are studied. It is proved that any compact analytic space has a formal versal associative deformation. Mathematics Subject Classi…cation (2000). 53D55, 13D10, 16S80, 81T70.

Stable Complex Manifolds

1. T. Van de Ven [3] has recently shown that there exist real 4dimensional manifolds which admit almost complex structures but admit no complex structures, e.g. SXS* # SXS # CP(2). The purpose of this note is to show that this is an unstable phenomenon. Let M be a C w-dimensional real manifold without boundary and let TM be its tangent bundle. R is real Euclidean fe-space and C is complex &-spa...

Dynamics of Automorphisms of Compact Complex Manifolds

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact Kähler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation between the dynamics of automorphisms/endomorphisms and the geometry of the underlying manifolds.

Neighborhoods of Analytic Varieties in Complex Manifolds

Non Compact Boundaries of Complex Analytic Varieties

Let M be a smooth and oriented real submanifold of some n-complex manifold X, of dimension 2m+ 1. A natural question occurs, whether M is the boundary of an (m + 1)-complex submanifold of X. This problem, called the boundary problem, has been extensively treated over the past fifty years when M is compact. The case m = 0, in X = C, has been first solved by Wermer [W] in 1958. Later on, in 1975,...