Abstract
In this paper, we mainly study the geometric model of the derived category of gentle one-cycle algebras provided by Opper, Plamondon and Schroll. We provide a realization of AAG-invariant on the surface, which is slightly different from the realization in their paper, and deduce a standard form of marked surfaces of gentle one-cycle algebras under derived equivalences. As an application, we classify those derived-unique gentle one-cycle algebras.
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