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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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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, S3 7RH, England, UK

    Tom Bridgeland

  2. Centre for Mathematical Sciences, Cambridge, CB3 0WB, England, UK

    Ivan Smith

Authors
  1. Tom Bridgeland
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  2. Ivan Smith
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Corresponding author

Correspondence to Tom Bridgeland.

Additional information

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

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