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I am a physics undergrad with no formal background in complex analysis. I have done complex analysis at the level of the first 4 chapters (till Complex integration) from Churchill and Brown. I am very keen to explore algebraic geometry, and I am thinking of starting with Rick Miranda's book on Algebraic Curves and Riemann Surfaces.

What are the complex analysis prerequisites for atleast starting this book (first 2-3 chapters)? Would first 4 chapters of Churchill and Brown be enough. If not, then what and from where should I study?

Also what are the topology prerequisite? I have done the 2nd chapter of Munkres? Is that enough?

Thanks.

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From amazon.com/Algebraic-Riemann-Surfaces-Graduate-Mathematics/dp/…: "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." –  Stahl Feb 21 '13 at 5:34

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