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arXiv · 2501.16903

Contractibility and total semi-stability conditions of Euclidean quivers

Yu Qiu·Xiaoting Zhang
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Abstract

We study the bounded derived category $\mathcal{D}$ of an Euclidean quiver, or equivalently, that of coherent sheaves on a tame weighted projective line. We give a description of the moduli space $\mathrm{ToSS}$ of the total semi-stability conditions on $\mathcal{D}$, which implies that $\mathrm{ToSS}$ can linearly contract to any chosen non-concentrated stability condition in it. For type $\widetilde{A_{p,q}}$, this gives an alternative proof of the contractibility of the whole space of stability conditions.

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BibTeXRIS

Yu Qiu, Xiaoting Zhang. 2025-01-28. Contractibility and total semi-stability conditions of Euclidean quivers. https://arxiv.org/abs/2501.16903

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