Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's   stability conditions
  Bridgeland stability condition is preserved under the Fourier-Mukai transform by its definition. We explain the relation with Gieseker stability. By studying the wall-crossing behavior, we reprove that the moduli spaces of stable sheaves on abelian surfaces are birationally equivalent, if the associated Mukai vectors are related by isometries of the Mukai lattice. 
Hiroki Minamide, Shintarou Yanagida, Kota Yoshioka
math.AG