2024/07/25 by Berman, Leah, Lundqvist, Signe, Schulze, Bernd +4
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2407.17836
In this paper, we establish a general setup for studying incidence-preserving motions of projective geometric configurations of points and lines via a "projective rigidity matrix". The spaces of infinitesimal motions of a point-line configuration and dependencies amongst the point-line incidences can be interpreted as the kernel and co-kernel of this projective rigidity matrix, respectively. We also introduce a symmetry-adapted projective rigidity matrix for analysing symmetric configurations and their symmetry-preserving motions. The symmetry may be a point group or a more general symmetry, such as an autopolarity.