Study On Second Main Theorem For Meromorphic Mappings From C~m To Algebraic Variety

Moving target is one of the important research problems on Nevanlinna theory for holomorphic curve.Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009,recently there has been some developments on the second main theorem into projective space and algebraic varieties intersecting moving hypersurfaces targets.Through further exploration,we have also got some new improvements.In this thesis,we mainly aim to give the second basic theorem about the index of moving hypersurface in the subgeneral position.In the first chapter,we firstly introduce the background and origin of Nevanlin-na's theory.Second,we introduce the research progress of the second main theorem for holomorphic curves to projective space and algebraic variety.The second chapter is preliminaries on some basic knowledge,which introduce-es some classical Nevanlinna theory and some basic knowledge in high dimension.The third chapter is the proof of the second main theorem to algebraic variety.The fourth chapter is the proof of the second main theorem with truncated multiplicity to projective space.The fifth chapter is the summary and prospect.On the one hand,it summarizes the thesis,on the other hand,it puts forward some problems to be solved in the future.