The Igusa Quartic and Borcherds Products

Abstract

By applying the theory of Borcherds of automorphic forms on bounded symmetric domains of type IV, we construct a 5-dimensional linear system of automorphic forms of weight 6 on the Igusa quartic 3-fold which defines an $\mathfrak{S}$ ₆-equivariant rational map of degree 16 from the Igusa quartic to the Segre cubic. In particular, it gives a rational self-map of the Igusa quartic of degree 16.