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Title:
Symplectic manifolds as obstructions to the projectivity of compact Kaehler Manifolds
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Abstract:
The role of holomorphic two-forms as obstructions to projectivity of a compact Kaehler manifold X is since long well-known from a famous theorem of Kodaira. A Kaehler version of the minimal model program would imply that any such X should be (holomorphically) symplectic, or a torus, if 'simple' (which means: of dimension at least 2, and not covered by closed suvarieties of pure intermediate dimension). This would imply an extremely short decomposition of any such X in terms of Tori, symplectic, and projective manifolds
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