... component of type (i), then the intersection in codimensionone of any two distinct components can only be a line.If there is no component of type (i), then the intersection in codimensionone of ... X2meeting along a conic. If there are THE K2 OF DEGENERATIONS OF SURFACES361other components, then there is a component Xmeeting all the rest along aline. Thus, the hyperplane section contains ... hyperplanesection D of X is not a cycle or there is an irreducible component of D whichis not rational, then D is not Gorenstein (see the discussion at the end of Example 2.7), contradicting the assumption...