The bicanonical map of the Cartwright-Steger surface

TL;DR

This paper proves that the bicanonical map of the Cartwright-Steger surface is an embedding and explores related minimal surfaces of general type with specific invariants.

Contribution

It establishes the embedding property of the bicanonical map for the Cartwright-Steger surface and analyzes two related minimal surfaces of general type.

Findings

The bicanonical map of the Cartwright-Steger surface is an embedding.

Identified two minimal surfaces of general type covered by the Cartwright-Steger surface.

Described properties of these minimal surfaces, including invariants like K^2 and p_g.

Abstract

We prove that the bicanonical map of the Cartwright-Steger surface is an embedding. We also discuss two minimal surfaces of general type, both covered by the Cartwright-Steger surface. One has $K^2=2$, $p_g=1$, $\pi_1=\{1\}$ and the other has $K^2=1$, $p_g=0$, $\pi_1=\mathbb{Z}/2\mathbb{Z}$.