Moishezon manifolds
Copyright policy )Moishezon manifolds
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 $��:X \to X'$ onto a projective variety X' with $��(Y)$ a point, such that $Pic(X/X') = \Z$ and $K_X$ is $��$-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
- University of Trento Italy
compact Moishezon manifold, \(n\)-folds (\(n>4\)), Global differential geometry of Hermitian and Kählerian manifolds, smooth subvariety, Compact complex \(n\)-folds, Mathematics - Algebraic Geometry, 14J40, 32J18, 53C55, 14E30, inequalities, FOS: Mathematics, dimensions, Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG)
compact Moishezon manifold, \(n\)-folds (\(n>4\)), Global differential geometry of Hermitian and Kählerian manifolds, smooth subvariety, Compact complex \(n\)-folds, Mathematics - Algebraic Geometry, 14J40, 32J18, 53C55, 14E30, inequalities, FOS: Mathematics, dimensions, Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG)
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