Cohomologies of complex manifolds with symplectic $(1,1)$-forms

Adriano Tomassini, Xu Wang

Let $(X,J)$ be a complex manifold with a non-degenerated smooth $d$-closed $(1,1)$-form $\omega$. Then we have a natural double complex $\overline{\partial }+{\overline{\partial }}^{\Lambda }$, whe…