The nonprojective surface X which is flat over a nodal plane cubic curve C with consisting of two componentsprojective lines attached at two nodes, where the fibers over the smooth points being of C are chains of two lines, and the fibers over the nodes being are chains of three lines. Considering the degrees of line bundles over restricted to the components of the fibers shows that X cannot admit an ample line bundle.

The nonprojective surface X which is flat over a nodal plane cubic C with two components, the fibers over the smooth points being chains of three two lines, and the fibers over the nodes being chains of two three lines. Considering the degrees of line bundles over components of the fibers shows that X cannot admit an ample line bundle.

The nonprojective surface X which is flat over a nodal plane cubic C with two components, the fibers over the smooth points being chains of three lines, and the fibers over the nodes being chains of two lines. Considering the degrees of line bundles over components of the fibers shows that X cannot admit an ample line bundle.