Projectivity criterion of Moishezon spaces and density of projective symplectic varieties

Abstract

A singular Moishezon space is not projective even if it is Kaehler. This paper gives a projectivity criterion for Kaehler Moishezon spaces. We shall use this projectivity criterion to show the density of projective symplectic varieties in the Kuranishi family of a (singular) symplectic variety.

To appear in International J. Math. Theorem 6 holds under a weaker condition; a Kaehler Moishezon space is projective when it has only 1-rational singularities. Newly added is the proof that the quadratic form $q$ has signature $(3,B-3)$