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 \cite{QZZ}. Using the similar argument in \cite{BS, BMQS, CHQ}, we extend this identification to an isomorphism between the spaces of stability conditions and of quadratic differentials.