This booklet and the next moment quantity is an creation into sleek algebraic geometry. within the first quantity the equipment of homological algebra, idea of sheaves, and sheaf cohomology are constructed. those tools are vital for contemporary algebraic geometry, yet also they are basic for different branches of arithmetic and of significant curiosity of their own.
within the final bankruptcy of quantity I those suggestions 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 number of the smooth equipment were expected by way of them.
For this moment variation the textual content used to be thoroughly revised and corrected. the writer additionally further a brief part on moduli of elliptic curves with N-level constructions. This new paragraph anticipates the various ideas 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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