j-invariant and Borcherds Phi-function

TL;DR

This paper establishes a formula connecting the difference of j-invariants to the Borcherds Phi-function, an automorphic form that characterizes the discriminant divisor on the period domain for Enriques surfaces.

Contribution

It provides a novel explicit relation between j-invariants and the Borcherds Phi-function in the context of Enriques surfaces.

Findings

Derived a formula linking j-invariants and Borcherds Phi-function

Characterized the discriminant divisor using automorphic forms

Enhanced understanding of automorphic forms on Enriques surfaces

Abstract

We give a formula that relates the difference of the j-invariants with the Borcherds Phi-function, an automorphic form on the period domain for Enriques surfaces characterizing the discriminant divisor.