Let V be a smooth cubic in P and let X = F(V ) be the variety of lines on V . Thus X is a smooth four-dimensional subvariety of the grassmanian G(1, 5), more precisely, the zero locus of a section of SU, where U is the tautological rank-two bundle over G(1, 5). It is immediate from this description that the canonical class of X is trivial. Let F ⊂ V × X be the universal family of lines on V , a...
