Unstable blueprints can be shared

Abstract

This expository note illustrates toric perturbation and biased pairing theory to show that Artinian reductions of face rings of $2$-spheres that do not satisfy the Lefschetz property can be cut along a flat equator. This complements classical work of Bricard and Connelly, and exhibits a fundamental symmetry in non-rigid triangulations of spheres.

arXiv commentwrong tex file with spoilers. expository note. overlap with arXiv:1812.10454, arXiv:1906.05859

References in corpus (2)

• Combinatorial Lefschetz theorems beyond positivity
• FAQ on the g-theorem and the hard Lefschetz theorem for face rings