This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them. For this second edition the text was completely revised and corrected. The author also added a short section on moduli of elliptic curves with N-level structures. This new paragraph anticipates some of the techniques of volume II.
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流形作为局部环层空间：从坐标环（对象是仿射空间）到函数环（对象流形例如曲线）的转变。任意拓扑空间都可以看做为局部环层空间（X，0x），模层
评分流形作为局部环层空间：从坐标环（对象是仿射空间）到函数环（对象流形例如曲线）的转变。任意拓扑空间都可以看做为局部环层空间（X，0x），模层
评分流形作为局部环层空间：从坐标环（对象是仿射空间）到函数环（对象流形例如曲线）的转变。任意拓扑空间都可以看做为局部环层空间（X，0x），模层
评分流形作为局部环层空间：从坐标环（对象是仿射空间）到函数环（对象流形例如曲线）的转变。任意拓扑空间都可以看做为局部环层空间（X，0x），模层
评分流形作为局部环层空间：从坐标环（对象是仿射空间）到函数环（对象流形例如曲线）的转变。任意拓扑空间都可以看做为局部环层空间（X，0x），模层
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