# Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation

## TL;DR

This paper offers a geometric interpretation of the discrete Schwarzian KP equation using quadrangular point sets in projective and Moebius spaces, linking conformal and projective geometries through Desargues maps.

## Contribution

It introduces a novel geometric framework for understanding the discrete Schwarzian KP equation within projective and Moebius geometries.

## Key findings

- Geometric interpretation of the discrete Schwarzian KP equation in projective line
- Extension of interpretation to Moebius chain space
- Connection between conformal and projective geometries via Desargues maps

## Abstract

We present geometric interpretation of the discrete Schwarzian Kadomtsev-Petviashvili equation in terms of quadrangular set of points of a projective line. We give also the corresponding interpretation for the projective line considered as a Moebius chain space. In this way we incorporate the conformal geometry interpretation of the equation into the projective geometry approach via Desargues maps.