Algebraic Surfaces With Pluricanonical Map As Abel Cover Mapping

The main purpose of this thesis is to determine all the minimal general type algebraic surfaces with the pluricanonical maps as an Abel cover maps over the projective plane P2 and the local equations. Factually, only the bicanonical map can be realized as finite morphism over P2, and we show two possible candidates. In the paper, Du rong and Gao yun have determined all the minimal general type surfaces with the canonical maps as an Abel cover by utilizing the theory of Abel cover. This thesis can be seen as some kind of continuation of their work, and we find exactly only two isomorphic class of surfaces under the assumed condition. Finally, we apply the previous method to a generalized case, and then construct surfaces with equation aKX=bD=bφ*H.