PROJECTIVITY CRITERION OF MOISHEZON SPACES AND DENSITY OF PROJECTIVE SYMPLECTIC VARIETIES
By Y. Namikawa. 2001
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A Moishezon manifold is a projective manifold if and only if it is a Kahler manifold [13]. However, a singular Moishezon space is not generally projective even if it is a Kahler space [14]. Vuono [19] has given a projectivity criterion for Moishezon spaces with isolated singularities. In this paper we shall prove that a Moishezon space with 1-rational singularities is projective when it is a Kahler space (Theorem 1.6). We shall use Theorem 1.6 to show the density of projective symplectic varieties in the Kuranishi family of a (singular) symplectic variety (Theorem 2.4), which is a generalization of the result by Fujiki [4, Theorem 4.8] to the singular case. In the Appendix we give a supplement and a correction to the previous paper [15] where singular symplectic varieties are dealt with.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/6e899a89e0ee4f0d65e95ed97406613bcad12439
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The global moduli theory of symplectic varieties (2018, background): “ini{Hacon{McKernan [BCHM10] on the termination of an appropriate version of the MMP, but it is not even clear a priori that a symplectic variety can be deformed to a projective one (although Namikawa [Nam02] has results in this direction). For this reason, we need a projectivity criterion for symple”