Freely acting Z3 symmetries of a Yau manifold and three-generation superstring models

We identify the various freely acting non-conjugate Z₃ symmetries of a Yau manifold defined by polynomials of bidegree (3, 0), (0, 3) and (1, 1) in CP³ × CP³. Compactification of the ten-dimensional heterotic superstring theory on this manifold, after dividing the latter out by one of these Z₃'s, gives rise to three physically distinct three-generation superstring models. One of them has not been previously identified and we discuss its residual four-dimensional discrete symmetries.