Abstract:

We study Bridgeland stability conditions on a Calabi-Yau-N category associated to the module over the dg Ginzburg algebra of the affine A_n quiver which can be geometrically realized by meromorphic quadratic differentials on Riemann surfaces. We will establish a relationship between the space of stability conditions of derived categories of quiver algebras and the space of quadratic differentials by considering the set of coloured quiver mutation classes. In addition, we determine the auto-equivalence group as the extended braid group of affine type A.