New reflective modular forms and modular varieties of Calabi-Yau type

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 very special cases, it is equal to zero. We construct three new strongly reflective modular forms of singular weight with $10$, $8$ and $6$ variables which produce three towers (8+3+4) of strongly reflective modular forms with the simplest possible divisor. The reflective  forms determine $15$ Lorentzian Kac-Moody super Lie algebras of Borcherds type.  Moreover we obtain three modular varieties of dimension $4$, $6$ and $7$ of Kodaira dimension $0$.