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arXiv · 2608.22208

Point Counts of Cluster Varieties of Marked Surfaces Over Finite Fields

James Beyer
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Abstract

We establish formulae for point counts of cluster varieties of cluster algebras of marked surfaces, possibly with punctures. We then establish formulae for the number of non-deep points in these cluster varieties over $\mathbb{F}_2$, which gives us the number of algebraic tori necessary to cover the cluster manifold over $\mathbb{F}_2$. We also show that these formulae satisfy certain recurrence relations.

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James Beyer. 2026-08-23. Point Counts of Cluster Varieties of Marked Surfaces Over Finite Fields. https://arxiv.org/abs/2608.22208

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