Friedman [Fr] has studied the relationship between local and global deformations of a threefold Z with isolated hypersurface singularities which admits small resolutions. One of his main results is as follows. Let Z be a Moishezon threefold with only ordinary double points {P_1....,P_n}. Assume that the canonical line bundel K_Z of Z is trivial. Let π:Z-Z be a small resolution and let C1:=π~(-1)(pi)=P1 be the exceptional curves. Then he showd that if there is a relation Σ1≦i≦n~(Xi)[C_1]=0 with x1=0. On the other hadn, Clements has compared the topology of Z with that of Zt=f~(-1)(t) in [Cl]. We have a simple relation e(Z)=e(Z_1)+2n for the Euler numbers. However, the relations between Betti numbers are not so ingte; there is a phenomenon called the defect of singularities. (See also [W], [Di].)
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