D Matsushita
AMERICAN JOURNAL OF MATHEMATICS 127 (2) 243 - 259 0002-9327 2005/04
[Refereed][Not invited] Let f : X -> S be a Lagrangian fibration between projective varieties. We prove that R-f(i)*O-X congruent to Omega(S)(i) if S is smooth. Suppose that X is an irreducible symplectic manifold or a certain moduli space of semistable torsion free sheaves on a K3 surface, the Hodge numbers satisfy h(p,q)(S) = h(p,q)(P-n), where n = dimS. If S congruent to P-n and X is an irreducible symplectic manifold, there exists a hypersurface M-f of the Kuranishi space of X such that every member of the Kuranishi family over Mf admits a Lagrangian fibration over P-n.