Quadratic differentials as stability conditions
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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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This is the author accepted manuscript. The final version is available from Springer via http://dx.doi.org/10.1007/s10240-014-0066-5TI
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Publications mathématiques de l'IHÉS
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121
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Springer
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Sponsorship
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.