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
Similar Algebraic Geometry books
Algebraic topology is a uncomplicated a part of smooth arithmetic, and a few wisdom of this sector is essential for any complicated paintings when it comes to geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This booklet presents an in depth remedy of algebraic topology either for academics of the topic and for complex graduate scholars in arithmetic both focusing on this region or carrying on with directly to different fields.
First textbook-level account of easy examples and strategies during this region. compatible for self-study by means of a reader who is aware a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yankee Mathematical Society, in addition to a profitable Springer writer.
Grothendieck’s appealing idea of schemes permeates sleek algebraic geometry and underlies its purposes to quantity idea, physics, and utilized arithmetic. this easy account of that concept emphasizes and explains the common geometric recommendations at the back of the definitions. within the e-book, suggestions are illustrated with basic examples, and particular calculations express how the structures of scheme idea are conducted in perform.
This vintage textual content, written through one of many prime mathematicians of the 20 th century, is now to be had in a low in cost paperback version. Exposition is headquartered at the foundations of affine geometry, the geometry of quadratic varieties, and the constitution of the overall linear team. Context is broadened through the inclusion of projective and symplectic geometry and the constitution of symplectic and orthogonal teams.
Extra info for Lectures on Algebraic Geometry I: Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces (Aspects of Mathematics)