Algebraically rigid simplicial complexes and graphs
Commutative Algebra
2021-04-07 v3
Abstract
We call a simplicial complex algebraically rigid if its Stanley-Reisner ring admits no nontrivial infinitesimal deformations, and call it inseparable if does not allow any deformation to other simplicial complexes. Algebraically rigid simplicial complexes are inseparable. In this paper we study inseparability and rigidity of Stanley-Reisner rings, and apply the general theory to letterplace ideals as well as to edge ideals of graphs. Classes of algebraically rigid simplicial complexes and graphs are identified.
Cite
@article{arxiv.1503.08080,
title = {Algebraically rigid simplicial complexes and graphs},
author = {Klaus Altmann and Mina Bigdeli and Juergen Herzog and Dancheng Lu},
journal= {arXiv preprint arXiv:1503.08080},
year = {2021}
}
Comments
25 pages to be appeared on JPAA