Every Riemann surface is a complex algebraic curve and every compact . in Rick Miranda’s book “Algebraic Curves and Riemann Surfaces”). Algebraic Curves and Riemann Surfaces. Rick Miranda. Graduate Studies in Mathematics. Volume 5. If American Mathematical Society. Author: Rick Miranda Title: Algebraic Curves and Riemann Surfaces Amazon Link.
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In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage.
This means we can study the same objects using both complex analysis and abstract algebra. After defining these objects carefully and showing how to construct examples, some of the questions we will discuss are: What are the complex analysis prerequisites for atleast starting this book first chapters?
Multiplicies and degrees F Feb 12 For simplicity, I’ll just talk about varieties that are sitting in projective space or affine space. Take-home, assigned March 7, due March Want to Read saving…. Martijn added it May 20, I have done complex analysis at the level of the first 4 chapters till Complex integration from Churchill and Brown. There are lots of gems in this short statement.
MATH 510: Riemann Surfaces and Algebraic Curves (Spring 2016)
Now the people call it a surface because it looks two-dimensional from surfsces real point of view. The book’s goal is to provide readers an overview what the zoo of curves looks like. Randomblue 1, 6 26 One of the best introductory textbooks on the theory of algebraic curves and Riemann surfaces … very well organized … plenty of examples … strongly recommend this book as a textbook for an introduction to algebraic curves and Riemann surfaces … One of my students said that surfwces is one of a very few books in algebraic geometry that he can read and understand.
This shouldn’t be too surprising. Is the result you alluded to called Riemann-Roch?
The hyperelliptic case is not hard to understand. Covering spaces and monodromy M Mar 7 Has a perspective and charm that makes it an excellent addition to the survey literature on the subject … a leisurely and well-presented introduction to algebraic geometry through the study of algebraic curves over the complex numbers … contains an abundance of examples and problems and develops the basic notions … thoroughly and carefully … excellent for self-study by beginners in the field … repays examination by anyone interested in the field for some interesting insights and for a number of excellent ideas about the development and presentation of the material … a charming book … [recommended] both to those advanced undergraduates who have an interest in this area and to any graduate students who wish to learn more about this important and lively area of mathematics … both beginners and experts as well will find a number of fascinating topics that do not normally appear in introductory texts.
Sign up or log in Sign up using Google. Winston marked it as to-read Jul 16, Gives a very readable account of Riemann Surfaces – a good course in complex analysis is all that’s required as a prereq. Quotients notes above F Mar 4 Dirichlet’s principle is an existence theorem for harmonic functions; this is relevant because harmonic functions on Riemann surfaces can be locally completed to holomorphic functions, and thus to meromorphic functions globally if topology allows a question of monodromy.
Algebraic Curves and Riemann Surfaces by Miranda | Physics Forums
Return to Book Page. See our librarian page for additional eBook ordering options. This gives some number, which could be 0, 1, 2, etc. I’m taking introductory courses in both Riemann surfaces and algebraic geometry this term. To recap, this a a geometry locally defined by algebraic equations in some space so that the resulting manifold is one-dimensional.
Homework 5Due Wednesday, April Among the iremann ways to start learning algebraic geometry let’s say we selected the abstract definition of an algebraic curve. The theories of compact Riemann surfaces and complex smooth projective algebraic curves are equivalent in a precise sense. Apparently deeper links exist.
Home Questions Tags Users Unanswered. Now, in its evolved and fully ripe form, the text impressively reflects his apparently outstanding teaching skills as well as his admirable ability for combining great expertise in the field with masterly aptitude for representation and didactical sensibility. In general, the converse is false: When are two Riemann surfaces isomorphic?
Want to Read Currently Reading Read. Integration F Apr 1 It turns out this is exactly the same thing though defined in a completely different way by a completely different branch of mathematics.