# Quadratic differentials as stability conditions

@article{Bridgeland2013QuadraticDA, title={Quadratic differentials as stability conditions}, author={Tom Bridgeland and Ivan Smith}, journal={Publications math{\'e}matiques de l'IH{\'E}S}, year={2013}, volume={121}, pages={155-278} }

We prove that moduli spaces of meromorphic quadratic differentials with simple zeroes on compact Riemann surfaces can be identified with spaces of stability conditions on a class of CY3 triangulated categories defined using quivers with potential associated to triangulated surfaces. We relate the finite-length trajectories of such quadratic differentials to the stable objects of the corresponding stability condition.

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