Abstract
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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During the writing of this paper T.B. was supported by All Souls College, Oxford.
I.S. was partially supported by a grant from the European Research Council.
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Bridgeland, T., Smith, I. Quadratic differentials as stability conditions. Publ.math.IHES 121, 155–278 (2015). https://doi.org/10.1007/s10240-014-0066-5
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DOI: https://doi.org/10.1007/s10240-014-0066-5