Pluricanonical maps for threefolds of general type and the Gromov-Witten potential for the local projective line with weights one and two

This thesis will contain two independent parts. In the first part we will prove that for threefolds of large volume the fifth pluricanonical map is birational. In the second part we will compute the Gromov-Witten potential of the local projective line with weights one and two.