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arXiv · 2407.17836

Projective rigidity of point-line configurations in the plane

Leah Berman·Signe Lundqvist·Bernd Schulze·Brigitte Servatius·Herman Servatius·Klara Stokes·Walter Whiteley
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Abstract

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.

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BibTeXRIS

Leah Berman, Signe Lundqvist, Bernd Schulze, Brigitte Servatius, Herman Servatius, Klara Stokes, Walter Whiteley. 2024-07-25. Projective rigidity of point-line configurations in the plane. https://arxiv.org/abs/2407.17836

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