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Oberseminar SoSe 2008 Abstract to the talk by Y. Nagai (Mainz)

On monodromies of a degeneration of irreducible symplectic Kähler manifolds

We consider a degeneration of an irreducible symplectic Kähler manifold and the associated monodromy operator on the Betti cohomology groups. In particular, we will discuss about the unipotency of the monodromy operators as invariants of a degeneration, which should be related to some topological/combinatorial data of the degenerate fiber. After looking at some examples, we observe that the unipotency of the (non-trivial) monodromy cannot be less than half of the weight of the cohomology group assuming that there exists a 'good' semistable degeneraton, which is analogous to the Kulikov-Persson-Pinkham degeneration of K3 surfaces.