Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality
Commutative Algebra
2015-08-25 v2
Abstract
We give an explicit presentation for each lower bound cluster algebra. Using this presentation, we show that each lower bound algebra Grobner degenerates to the Stanley-Reisner scheme of a vertex-decomposable ball or sphere, and is thus Cohen-Macaulay. Finally, we use Stanley-Reisner combinatorics and a result of Knutson-Lam-Speyer to show that all lower bound algebras are normal.
Cite
@article{arxiv.1508.02314,
title = {Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality},
author = {Greg Muller and Jenna Rajchgot and Bradley Zykoski},
journal= {arXiv preprint arXiv:1508.02314},
year = {2015}
}
Comments
16 pages