Igusa quartic and Borcherds products

TL;DR

This paper constructs a 5-dimensional linear system of automorphic forms on the Igusa quartic using Borcherds' theory, leading to an S_6-equivariant rational map to the Segre cubic.

Contribution

It introduces a novel automorphic form construction on the Igusa quartic and establishes a new degree-16 rational map to the Segre cubic.

Findings

Constructed a 5-dimensional automorphic form system of weight 6

Established an S_6-equivariant rational map of degree 16

Connected Igusa quartic with Segre cubic via automorphic forms

Abstract

By applying Borcherds' theory of automorphic forms on bounded symmetric domains of type IV, we give a 5-dimensional linear system of automorphic forms of weight 6 on Igusa quartic 3-fold which induces an S_6-equivariant rational map of degree 16 from Igusa quartic to Segre cubic.