Journal of Symplectic Geometry

Volume 3 (2005)

Number 3

Symplectic Deformations of Kähler Manifolds

Pages: 341 – 355

DOI: http://dx.doi.org/10.4310/JSG.2005.v3.n3.a2

Author

Paolo de Bartolomeis

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.

Full Text (PDF format)