In this paper, we study complex symplectic manifolds, i.e., compact complex manifolds X which admit a holomorphic (2, 0)-form σ which is d-closed and non-degenerate, and in particular the Beauville–Bogomolov–Fujiki quadric Qσ associated with them. We will show that if X satisfies the -lemma, then Qσ is smooth if and only if h2 , 0(X) = 1 and is irreducible if and only if h1 , 1(X) > 0.
Complex symplectic structures and the del-delbar-lemma
Cattaneo A.;
2018
Abstract
In this paper, we study complex symplectic manifolds, i.e., compact complex manifolds X which admit a holomorphic (2, 0)-form σ which is d-closed and non-degenerate, and in particular the Beauville–Bogomolov–Fujiki quadric Qσ associated with them. We will show that if X satisfies the -lemma, then Qσ is smooth if and only if h2 , 0(X) = 1 and is irreducible if and only if h1 , 1(X) > 0.
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