Geodesic
Quadratic differentials as stability conditions
Bridgeland, Tom1  ; Smith, Ivan2
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
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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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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