On Geometric Models of String Algebras: Uniqueness of Surfaces and Existence of Red Punctures

Zheng Xin; Lingchun Zhang

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arXiv · 2608.14360

On Geometric Models of String Algebras: Uniqueness of Surfaces and Existence of Red Punctures

Zheng Xin·Lingchun Zhang

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Abstract

A geometric model for string algebras was recently established in \cite{BC24}. Building upon this framework, we characterize the class of string algebras whose geometric models are unique up to equivalence of labelled tiled surfaces. Moreover, we provide a necessary and sufficient condition for all geometric models of a string algebra to be entirely free of red punctures, and further give a combinatorial description of string algebras with a common red puncture across all geometric models. In addition, we derive a sufficient condition for a string algebra guaranteeing the presence of red punctures in all geometric models.

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BibTeX RIS

Zheng Xin, Lingchun Zhang. 2026-08-14. On Geometric Models of String Algebras: Uniqueness of Surfaces and Existence of Red Punctures. https://arxiv.org/abs/2608.14360

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