TL;DR
This paper constructs a 5-dimensional space of automorphic forms on a complex ball using Borcherds theory, revealing a dual map between the Segre cubic and Igusa quartic threefolds.
Contribution
It introduces a novel construction of automorphic forms that connects the Segre cubic and Igusa quartic via a dual map.
Findings
Established a 5-dimensional automorphic form system on a complex ball.
Connected the Segre cubic to the Igusa quartic through the dual map.
Applied Borcherds theory to geometric and automorphic form relationships.
Abstract
We shall construct a 5-dimensional linear system of holomorphic automorphic forms on a 3-dimensional complex ball by applying Borcherds theory of automorphic forms. We shall show that this linear system gives the dual map from the Segre cubic 3-fold to the Igusa quartic 3-fold.
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