Geodesic
Integrable symplectic structures on compact complex manifolds
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 459-469

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The following question is studied. Suppose one is given a $2n$-dimensional compact complex manifold with holomorphic symplectic 2-form. Are there obstructions to the existence of $n$ independent meromorphic first integrals in involution, and if so, what are they like? The answer to this question is given for K3 surfaces, Beauville manifolds, and complex tori; in these cases there are obstructions of an analytic character. Whether there are any topological obstructions is an unsolved problem. Bibliography: 18 titles. 
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     author = {D. G. Markushevich},
     title = {Integrable symplectic structures on compact complex manifolds},
     journal = {Sbornik. Mathematics},
     pages = {459--469},
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     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a11/}
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D. G. Markushevich. Integrable symplectic structures on compact complex manifolds. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 459-469. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a11/