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arXiv · 1411.4003

Decorated marked surfaces II: Intersection numbers and dimensions of Homs

Yu Qiu·Yu Zhou
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Abstract

We study the 3-Calabi-Yau categories $\mathcal{D}$ arising from quivers with potential associated to a decorated marked surface $\mathbf{S}_\bigtriangleup$ introduced by the first author. We prove two conjectures in the prequel, that under a bijection between certain objects in $\mathcal{D}$ and certain arcs in $\mathbf{S}_\bigtriangleup$, the dimensions of morphisms between these objects equal the intersection numbers between the corresponding arcs.

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Yu Qiu, Yu Zhou. 2017-06-02. Decorated marked surfaces II: Intersection numbers and dimensions of Homs. https://arxiv.org/abs/1411.4003

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