Deformation classes of real Cayley M-octads

TL;DR

This paper classifies and analyzes the deformation classes of specific 8-point configurations in real projective space, revealing 8 mirror-pairs, their mutual positions, and associated monodromy groups.

Contribution

It provides a complete classification of deformation classes of 8-point configurations formed by intersections of three quadrics in real projective space, including their monodromy groups.

Findings

Exactly 8 mirror-pairs of deformation classes identified

Descriptions of mutual positions of these pairs provided

Real monodromy groups acting on configurations characterized

Abstract

We study 8-point configurations in the real projective space forming an intersection locus of three quadrics and containing no coplanar quadruples. We found that there exists precisely 8 mirror-pairs of deformation classes of such configurations. We describe also the mutual position of these 8 pairs and find the real monodromy groups acting on the 8-point configurations, for each deformation class.