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arXiv · 2501.00435

The quiver with superpotentials of a $d$-angulation of a marked surface

Bo Le·Bin Zhu
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Abstract

In this paper, we associate a quiver with superpotential to each $d$-angulation of a (unpunctured) marked surface. We show that, under quasi-isomorphisms, the flip of a $d$-angulation is compatible with Oppermann's mutation of (the Ginzburg algebra of) the corresponding quiver with superpotential, thereby partially generalizing the result in [LF09]. Applying to the generalized $(d-2)$-cluster categories associated to this quiver with superpotential, we prove that some certain almost complete $(d-2)$-cluster tilting objects in the higher cluster category have exactly $d-1$ complements.

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Bo Le, Bin Zhu. 2024-12-31. The quiver with superpotentials of a $d$-angulation of a marked surface. https://arxiv.org/abs/2501.00435

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