Counter-example to global Torelli problem for irreducible symplectic manifolds
نویسنده
چکیده
A simply connected compact Kaehler manifold X is an irreducible symplectic manifold if there is an everywhere non-degenerate holomorphic 2-form Ω on X with H0(X,Ω2X) = C[Ω]. By definition, X has even complex dimension. There is a canonical symmetric form qX on H (X,Z), which is called the Beauville-Bogomolov form (cf. [Be]). On the other hands, since X is Kaehler, H(X,Z) has a natural Hodge structure of weight 2. If two irreducible symplectic manifolds X and Y are bimeromorphically equivalent, then there is a natural Hodge isometry between (H(X,Z), qX) and (H (Y,Z), qY ) (cf. [O, Proposition (1.6.2)], [Huy, Lemma 2.6]). In this paper we shall give a counter-example to the following problem of Torelli type (cf. [Mu], [Huy])
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