Algebraic Curves and Riemann Surfaces (Graduate Studies in

Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5) (Graduate Studies in Mathematics, 5)
- Used Book in Good Condition
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of a one semester of complex variable! theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.
Country USA
Brand Brand: American Mathematical Society
Manufacturer American Mathematical Society
Binding Hardcover
ItemPartNumber 646806
ReleaseDate 1995-04-01
UnitCount 1
EANs 9780821802687

Country	USA
Brand	Brand: American Mathematical Society
Manufacturer	American Mathematical Society
Binding	Hardcover
ItemPartNumber	646806
ReleaseDate	1995-04-01
UnitCount	1
EANs	9780821802687

Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5) (Graduate Studies in Mathematics, 5)