Finite type and completeness of $g$-fans

Toshiya Yurikusa

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arXiv · 2512.21603

Finite type and completeness of $g$-fans

Toshiya Yurikusa

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Abstract

We study the $g$-fan associated with a skew-symmetrizable matrix in the sense of cluster algebras. We show that a skew-symmetrizable matrix is of finite type if and only if its $g$-fan is complete; equivalently (as we show), its support contains all lattice points.

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BibTeX RIS

Toshiya Yurikusa. 2025-12-25. Finite type and completeness of $g$-fans. https://arxiv.org/abs/2512.21603

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