Decorated marked surfaces II: Intersection numbers and dimensions of Homs

Qiu, Yu; Zhou, Yu

doi:10.1090/tran/7598

Decorated marked surfaces II: Intersection numbers and dimensions of Homs
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by Yu Qiu and Yu Zhou PDF

Trans. Amer. Math. Soc. 372 (2019), 635-660 Request permission

Abstract:

We study derived categories arising from quivers with potential associated to a decorated marked surface $\mathbf {S}_\bigtriangleup$, in the sense taken in a paper by Qiu. We prove two conjectures from Qiu’s paper in which, under a bijection between certain objects in these categories 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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