Toric systems and mirror symmetry
  Hille and Perling associate to every cyclic full strongly exceptional sequence of line bundles on a toric weak Fano surface a toric system, which defines a new toric surface. In this note we interprete this construction as an instance of mirror symmetry and extend it to a duality on the set toric weak Fano surfaces equiped with a cyclic full strongly exceptional sequence. 
Raf Bocklandt
math.AG math.RT