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.

Résumé

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.

Détail

DOI : 10.1007/s10240-014-0066-5

Keywords: Riemann Surface, Marked Point, Boundary Component, Quadratic Differential, Simple Object

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