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The Nash Conjecture for Nonprojective Threefolds

János Kollár
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Abstract

We prove that for every compact, connected, differentiable 3--manifold $M$ there is a compact complex manifold $X$ which can be obtained from projective 3--space by a sequence of smooth, real blow ups and downs such that $M$ is diffeomorphic to the set of real points of $X$. By earlier results, such an $X$ can almost never be projective.

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János Kollár. 2000-09-11. The Nash Conjecture for Nonprojective Threefolds. https://arxiv.org/abs/math/0009108

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