On Moduli Spaces Of Coherent Sheaves Over Del Pezzo Surfaces

In this thesis we prove that there exists a monadfriendly exceptional sequence on the derived category of coherent sheaves of Del Pezzo surface X₃.This establishes the isomorphism between the moduli space of some classes of the Gieseker-?semi?stable coherent sheaves to the moduli space of ?G,?-?semi?stable representations of some quiver?Q,J?.We also compute explicitly the quiver Q in the case of X₃.