This booklet and the next moment quantity is an creation into sleek algebraic geometry. within the first quantity the tools of homological algebra, conception of sheaves, and sheaf cohomology are constructed. those equipment are integral for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of significant curiosity of their own.

within the final bankruptcy of quantity I those strategies are utilized to the speculation of compact Riemann surfaces. during this bankruptcy the writer makes transparent how influential the information of Abel, Riemann and Jacobi have been and that the various sleek equipment were expected by means of them.

For this moment version the textual content was once thoroughly revised and corrected. the writer additionally further a brief part on moduli of elliptic curves with N-level buildings. This new paragraph anticipates the various options of quantity II.

**Read Online or Download Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics) PDF**

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