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.
@article{PMIHES_2015__121__155_0, author = {Bridgeland, Tom and Smith, Ivan}, title = {Quadratic differentials as stability conditions}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {155--278}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {121}, year = {2015}, doi = {10.1007/s10240-014-0066-5}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-014-0066-5/} }
TY - JOUR AU - Bridgeland, Tom AU - Smith, Ivan TI - Quadratic differentials as stability conditions JO - Publications Mathématiques de l'IHÉS PY - 2015 SP - 155 EP - 278 VL - 121 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - http://www.numdam.org/articles/10.1007/s10240-014-0066-5/ DO - 10.1007/s10240-014-0066-5 LA - en ID - PMIHES_2015__121__155_0 ER -
%0 Journal Article %A Bridgeland, Tom %A Smith, Ivan %T Quadratic differentials as stability conditions %J Publications Mathématiques de l'IHÉS %D 2015 %P 155-278 %V 121 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U http://www.numdam.org/articles/10.1007/s10240-014-0066-5/ %R 10.1007/s10240-014-0066-5 %G en %F PMIHES_2015__121__155_0
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. http://www.numdam.org/articles/10.1007/s10240-014-0066-5/
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