Geodesic
Quadratic differentials as stability conditions
Bridgeland, Tom1 idref ; Smith, Ivan2
1School of Mathematics and Statistics, University of Sheffield Hicks Building S3 7RH Hounsfield Road England UK
2Centre for Mathematical Sciences CB3 0WB Cambridge England UK
Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 155-278
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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.

DOI : 10.1007/s10240-014-0066-5
Keywords: Riemann Surface, Marked Point, Boundary Component, Quadratic Differential, Simple Object

Bridgeland, Tom  1   ; Smith, Ivan  2

1 School of Mathematics and Statistics, University of Sheffield Hicks Building S3 7RH Hounsfield Road England UK
2 Centre for Mathematical Sciences CB3 0WB Cambridge England UK 
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     title = {Quadratic differentials as stability conditions},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {155--278},
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Bridgeland, Tom; Smith, Ivan. Quadratic differentials as stability conditions. Publications Mathématiques de l'IHÉS, Tome 121 (2015), pp. 155-278. doi: 10.1007/s10240-014-0066-5

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