  We prove that the existence of a strongly reflective modular form of a large
weight implies that the Kodaira dimension of the corresponding modular variety
is negative or, in some special case, it is equal to zero. Using the Jacobi
lifting we construct three towers of strongly reflective modular forms with the
simplest possible divisor. In particular we obtain a Jacobi lifting
construction of the Borcherds-Enriques modular form Phi_4 and Jacobi liftings
of automorphic discriminants of the K\"ahler moduli of Del Pezzo surfaces
constructed recently by Yoshikawa. We obtain also three modular varieties of
dimension 4, 6 and 7 of Kodaira dimension 0.
