Configurations of 10 points and their incidence varieties
Algebraic Geometry
2025-07-15 v1
Abstract
Incidence varieties are spaces of -tuples of points in the projective plane that satisfy a given set of collinearity conditions. We classify the components of incidence varieties and realization moduli spaces associated to configurations of up to 10 points, up to birational equivalence. We show that each realization space component is birational to a projective space, a genus 1 curve, or a K3 surface. To do this, we reduce the problem to a study of 163 special arrangements called superfigurations. Then we use computer algebra to describe the realization space of each superfiguration.
Keywords
Cite
@article{arxiv.2507.09829,
title = {Configurations of 10 points and their incidence varieties},
author = {Kelly Isham and Nathan Kaplan and Sam Kimport and Rachel Lawrence and Luke Peilen and Max Weinreich},
journal= {arXiv preprint arXiv:2507.09829},
year = {2025}
}
Comments
25 pages