The purpose of this paper to determine the complex projective space  as a complex manifold is to calculate the cohomology of the coherent sheaves of . The research method in this paper is to construct an -dimensional complex projective space, namely  and then the n-dimensional complex projective space, namely , is a complex manifold. The result of this research is the -dimensional complex projective space, namely is a complex and compact manifold.
                        
                        
                        
                        
                            
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