A tale of two surfaces

TL;DR

This paper explores a connection between the surface of cuboids and the Schoen surface, both of which relate to a specific algebraic surface with particular properties, revealing a shared geometric structure.

Contribution

It establishes a link between two recently studied surfaces, showing they produce a surface with q=4 and a specific canonical map, unifying their geometric features.

Findings

Both surfaces lead to a surface with q=4.

The canonical map is 2-to-1 onto an intersection of 4 quadrics in P^6.

The resulting surface has 48 nodes.

Abstract

We point out a link between two surfaces which have appeared recently in the literature: the surface of cuboids and the Schoen surface. Both surfaces give rise to a surface with q=4, whose canonical map is 2-to-1 onto an intersection of 4 quadrics in P^6 with 48 nodes.