Singularities of locally acyclic cluster algebras
Commutative Algebra
2016-01-20 v1 Algebraic Geometry
Abstract
We show that locally acyclic cluster algebras have (at worst) canonical singularities. In fact, we prove that locally acyclic cluster algebras of positive characteristic are strongly F-regular. In addition, we show that upper cluster algebras are always Frobenius split by a canonically defined splitting, and that they have a free canonical module of rank one. We also give examples to show that not all upper cluster algebras are F-regular if the local acyclicity is dropped.
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Cite
@article{arxiv.1404.4399,
title = {Singularities of locally acyclic cluster algebras},
author = {Angélica Benito and Greg Muller and Jenna Rajchgot and Karen E. Smith},
journal= {arXiv preprint arXiv:1404.4399},
year = {2016}
}
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24 pages