Factoriality of nodal three-dimensional varieties and connectedness of the locus of log canonical singularities

Shokurov's vanishing theorem is used for the proof of the Q-factoriality of the following nodal threefolds: a complete intersection of hypersurfaces F and G in P5 of degrees n and k, n≥k, such that G is smooth and |Sing(F intersection G)|≤(n+k-2)(n-1)/5; a double cover of a smooth hypersurface F subset of P4 of degree n branched over the surface cut on F by a hypersurface G subset of P4 of degree 2r≥n, provided that |Sing(F intersection G)|≤2r+n-2)r/4