2025/10/10 by Carlos Rito, Rito, Carlos, Xavier Roulleau +1
Computer Science · Mathematics · #20F05 #20F34 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Geometric and Algebraic Topology #Primary 14J29 #Secondary 14Q10
paper · pdf · doi:10.48550/arxiv.2510.09588
openalex publication_date 2025/10/10 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
Starting from computer experiments with the fundamental group of the Cartwright--Steger surface, we construct an infinite tower (Xn)n≥ 1 of normal projective surfaces obtained by successive \mathbb Z/3-Galois covers Xn→ Xn-1. For n>1, their minimal resolutions \widetildeXn lie on the line K2 = 9χ- 18 (equivalently c12 = 3c2 - 72), which is parallel to the Bogomolov--Miyaoka--Yau line K2 = 9χ of ball quotients. We compute the fundamental groups for the first cases, showing that π1(\widetildeXn)=1 for n=1,…,5. Motivated by the geometry of the construction, we conjecture that all \widetildeXn are simply connected.