Abstract
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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