Algebraic Curves And Riemann Surfaces (Graduate Studies In Mathematics, Vol 5) (Graduate Studies In Mathematics, 5)

Algebraic Curves And Riemann Surfaces (Graduate Studies In Mathematics, Vol 5) (Graduate Studies In Mathematics, 5)

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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 Riemannroch And Serre Duality Theorems Are Presented In An Algebraic Manner, Via An Adaptation Of The Adelic Proof, Expressed Completely In Terms Of Solving A Mittagleffler 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 Secondsemester Course In Complex Variables Or A Yearlong Course In Algebraic Geometry.

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Frequently Asked Questions

  • Q: What is the main focus of 'Algebraic Curves and Riemann Surfaces'? A: The book primarily focuses on introducing algebraic curves over complex numbers, integrating classical intuition about surfaces and integration with examples of Riemann surfaces.
  • Q: What prerequisites are needed to understand this book? A: A background in one semester of complex variable theory and a year of abstract algebra is required to grasp the concepts presented in this textbook.
  • Q: Who is the author of this book? A: The author of 'Algebraic Curves and Riemann Surfaces' is Rick Miranda.
  • Q: What is the binding type of this book? A: This book is available in hardcover binding.
  • Q: How many pages does this book have? A: The book contains a total of 390 pages.
  • Q: When was 'Algebraic Curves and Riemann Surfaces' published? A: The book was published on April 1, 1995.
  • Q: What condition is the book in? A: The item condition of this book is classified as 'New'.
  • Q: What are some key features of the book? A: A key feature of the book is its approach to presenting algebraic curves with numerous examples, making it suitable as a primer on Riemann surfaces.
  • Q: Is this book suitable for self-study? A: While it is structured as a graduate textbook, motivated readers with the necessary background in complex variables and abstract algebra may find it valuable for self-study.
  • Q: What topics does the book cover? A: The book covers topics such as Riemann surfaces, complex charts, meromorphic functions, projective curves, and proofs of the Riemann-Roch and Serre Duality Theorems.