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 Q_σ associated with them. We will show that if X satisfies the ∂∂¯ -lemma, then Q_σ is smooth if and only if h^(2,0)(X)=1 and is irreducible if and only if h^(1,1)(X)>0.
Complex symplectic structures and the partial derivative partial derivative-lemma / Cattaneo, Andrea; Tomassini, Adriano. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 197:1(2018), pp. 139-151. [10.1007/s10231-017-0672-1]
Complex symplectic structures and the partial derivative partial derivative-lemma
Cattaneo, Andrea
;Tomassini, Adriano
2018-01-01
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 Q_σ associated with them. We will show that if X satisfies the ∂∂¯ -lemma, then Q_σ is smooth if and only if h^(2,0)(X)=1 and is irreducible if and only if h^(1,1)(X)>0.File in questo prodotto:
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