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arXiv · 1508.02314

Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality

Greg Muller·Jenna Rajchgot·Bradley Zykoski
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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.

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Greg Muller, Jenna Rajchgot, Bradley Zykoski. 2015-08-10. Lower bound cluster algebras: presentations, Cohen-Macaulayness, and normality. https://arxiv.org/abs/1508.02314

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