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arXiv · 2106.06985

On maximal green sequence for quivers arising from weighted projective lines

Changjian Fu·Shengfei Geng
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Abstract

We investigate the existence and non-existence of maximal green sequences for quivers arising from weighted projective lines. Let $Q$ be the Gabreil quiver of the endomorphism algebra of a basic cluster-tilting object in the cluster category $\mathcal{C}_\mathbb{X}$ of a weighted projective line $\mathbb{X}$. It is proved that there exists a quiver $Q'$ in the mutation equivalence class $\operatorname{Mut}(Q)$ such that $Q'$ admits a maximal green sequence. On the other hand, there is a quiver in $\operatorname{Mut}(Q)$ which does not admit a maximal green sequence if and only if $\mathbb{X}$ is of wild type.

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BibTeXRIS

Changjian Fu, Shengfei Geng. 2021-06-13. On maximal green sequence for quivers arising from weighted projective lines. https://doi.org/10.1007/s10468-022-10152-3

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