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arXiv · 1404.4399

Singularities of locally acyclic cluster algebras

Angélica Benito·Greg Muller·Jenna Rajchgot·Karen E. Smith
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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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Angélica Benito, Greg Muller, Jenna Rajchgot, Karen E. Smith. 2014-04-16. Singularities of locally acyclic cluster algebras. https://doi.org/10.2140/ant.2015.9.913

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