Fundamental Group of Desargues Configuration Spaces

TL;DR

This paper calculates the fundamental groups of different Desargues configuration spaces in complex projective spaces, including planar and non-planar cases, with fixed or arbitrary centers, advancing understanding of their topological properties.

Contribution

It provides the first comprehensive computation of the fundamental groups for these configuration spaces, covering various geometric conditions.

Findings

Fundamental groups of planar Desargues configuration spaces are determined.

Fundamental groups of non-planar Desargues configuration spaces are computed.

Results reveal topological distinctions based on configuration constraints.

Abstract

We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.