Moishezon Manifolds

Abstract

Let X be a compact Moishezon manifold which becomes projective after blowing up a smooth subvariety $Y\subset X$. We assume also that there exists a proper map $\rho :X\to X^{\prime }$ onto a projective variety X' with $\rho (Y)$ a point, such that $Pic(X/X^{\prime })=\mathbb{Z}$ and $K_X$ is $\rho$-big. We prove some inequalities between the dimensions of Y and X and we construct examples which shows the optimality of the inequalities. Then we discuss some differential geometry properties of these examples which lead to a conjecture.

Plain-Tex, 10 pages