This booklet and the next moment quantity is an advent into sleek algebraic geometry. within the first quantity the equipment of homological algebra, conception of sheaves, and sheaf cohomology are constructed. those tools are imperative for contemporary algebraic geometry, yet also they are primary for different branches of arithmetic and of serious curiosity of their own.
within the final bankruptcy of quantity I those recommendations are utilized to the speculation of compact Riemann surfaces. during this bankruptcy the writer makes transparent how influential the guidelines of Abel, Riemann and Jacobi have been and that a few of the sleek equipment were expected by way of them.
For this moment version the textual content used to be thoroughly revised and corrected. the writer additionally additional a quick part on moduli of elliptic curves with N-level constructions. This new paragraph anticipates many of the strategies of quantity II.
Read or Download Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics) PDF
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