On monodromies of a degeneration of irreducible symplectic Kähler manifolds

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We study the monodromy operators on the betti cohomologies associated to a good degeneration of irreducible symplectic manifold and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension.
22 pages. To appear in Math. Z

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