\BOOKMARK [1][-]{section.1}{1. Sextic elliptic ruled surfaces and cubic fourfolds}{}% 1
\BOOKMARK [1][-]{section.2}{2. Constructing the del Pezzo fibration}{}% 2
\BOOKMARK [1][-]{section.3}{3. Rationality of sextic del Pezzo surfaces}{}% 3
\BOOKMARK [1][-]{section.4}{4. Rationality of our cubic fourfolds}{}% 4
\BOOKMARK [1][-]{section.5}{5. Singular fibers and discriminant curves}{}% 5
\BOOKMARK [1][-]{section.6}{6. An explicit example}{}% 6
\BOOKMARK [1][-]{section*.1}{References}{}% 7