Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras
Abstract
We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs, using the geometric models and the intersection formula in QZZ. Using the similar argument in BS, BMQS, CHQ, we extend this identification to an isomorphism between the spaces of stability conditions and of quadratic differentials.
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