A class of complex analytic foliate manifolds with rigid structure

Neighborhoods of Analytic Varieties in Complex Manifolds

Kähler Manifolds with Positive First Chern Class and Mirrors of Rigid Calabi–yau Manifolds

Recent work on the relation between a special class of Kähler manifolds with positive first Chern class and critical N=2 string vacua with c=9 is reviewed and extended. Based on a talk presented at the International Workshop on Supersymmetry and Unification of Fundamental Interactions (SUSY 93), Boston, MA, March 1993. This work was supported in part by NSF grant PHY–89–04035 Email address: net...

Baker-sprindžuk Conjectures for Complex Analytic Manifolds

The circle of problems that the present paper belongs to dates back to the 1930s, namely, to K. Mahler’s work on a classification of transcendental real and complex numbers. For a polynomial P (x) = a0 + a1x + · + anx n ∈ Z[x], let us denote by hP the height of P , that is, hP def = maxi=0,...,n |ai|. It can be easily shown using Dirichlet’s Principle that for any z ∈ C and any n ∈ N there exis...

Complex Analytic Manifolds without Countable Base

1. It has been shown by Radó3 that every Riemann surface satisfies Hausdorff's second countability axiom. In the same paper Radó gives a construction due to Prüfer of a real 2-dimensional locally Euclidean space whose open sets do not have a countable base. The purpose of this paper is to confirm a conjecture of Bochner that there exist non second-countable complex manifolds of complex dimensio...

Some Geometric and Analytic Properties of Homogeneous Complex Manifolds

This is the first of two papers dealing with homogeneous complex manifolds; since the second work is a continuation of this one, we shall let the following introduction serve for both. The general problem is to study the geometric, analytic, and function-theoretic properties of homogeneous complex manifolds. The present paper, referred to as Part I, is concerned mainly with sheaves and cohomolo...