Moishezon Manifolds

1997/02/04 by Andreatta, Marco · 1 citation
#14E30 #14J40 #32J18 #53C55 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9702005

Abstract

Let X be a compact Moishezon manifold which becomes projective after blowing up a smooth subvariety Y ⊂ X. We assume also that there exists a proper map ρ:X → X' onto a projective variety X' with ρ(Y) a point, such that Pic(X/X') = \Z and K_X is ρ-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.

Cited by

• p-Kähler structures on compact complex manifolds

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