Resultants and the Borcherds Phi-function

TL;DR

This paper provides an algebro-geometric construction of the Borcherds Phi-function, an automorphic form that characterizes the discriminant locus on the moduli space of Enriques surfaces.

Contribution

It introduces a novel algebro-geometric approach to constructing the Borcherds Phi-function, linking automorphic forms with algebraic geometry.

Findings

Explicit construction of the Borcherds Phi-function

Connection between automorphic forms and algebraic geometry

Characterization of the discriminant locus on Enriques surfaces

Abstract

The Borcherds Phi-function is the automorphic form on the moduli space of Enriques surfaces characterizing the discriminant locus. In this paper, we give an algebro-geometric construction of the Borcherds Phi-function.