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Working paper

Cohomological properties of Hermitian symplectic threefolds

Papayanov G.
A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form ω, for which the bilinear form ω(I·, ·) is positive definite. In this work we prove ddc -lemma for 1- and (1,1)-forms for compact Hermitian symplectic manifolds of dimension 3. This shows that Albanese map for such manifolds is well-defined and allows one to prove Kahlerness if the dimension of the Albanese image of a manifold is maximal.