A characterization of two classes of locally truncated diagram geometries

TL;DR

This paper investigates specific locally truncated geometries related to parapolar spaces, demonstrating their residual connectivity and their universal 2-covers as truncations of buildings, advancing understanding of their structural properties.

Contribution

It characterizes two classes of locally truncated diagram geometries, showing they are residually connected and their universal 2-covers are truncations of buildings, which is a novel structural insight.

Findings

Residually connected sheaves over these geometries are constructed.

These geometries are residually connected diagram geometries.

Universal 2-covers are truncations of buildings.

Abstract

We study locally truncated geometries that are parapolar spaces locally of type A_{n-1,j}(K) with n>6 and j=3,4. Residually connected sheaves over these geometries are constructed. It is proved that these geometries are residually connected diagram geometries whose universal 2-covers are truncations of buildings.