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Mathematische Zeitschrift

, Volume 258, Issue 2, pp 407–426 | Cite as

On monodromies of a degeneration of irreducible symplectic Kähler manifolds

  • Yasunari Nagai
Article

Abstract

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. This implies that the “mildest” singular fiber of a good degeneration with non-trivial monodromy of irreducible symplectic manifolds is quite different from the generic degeneration of abelian varieties or Calabi–Yau manifolds.

Mathematics Subject Classification (2000)

Primary 14D05 Secondary 14J32 Secondary 32Q20 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Korea Institute for Advanced Study (KIAS)SeoulSouth Korea

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