Symplectic Deformations of Kähler Manifolds

Abstract

Given a compact symplectic manifold $(M,\,\kappa)$, $H^{2}(M,\,{\Bbb{R}})$\, represents, in a natural sense, the tangent space of the moduli space of germs of deformations of the symplectic structure. In the case $(M,\,\kappa,\,J)$ is a compact Kähler manifold, the author provides a complete description of the subset of $H^{2}(M,\,{\Bbb{R}})$ corresponding to Kähler deformations, including the non-generic case, where (at least locally) some hyperkähler manifold factors out from $M$. Several examples are also discussed.