Fourier-Mukai transforms and the wall-crossing behavior for Bridgeland's stability conditions

Understand

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.