Learn Algebraic Geometry: Books for Prep & Study

  • Thread starter Tibarn
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In summary, algebraic geometry is a branch of mathematics that uses algebraic tools to study the solutions to polynomial equations. It has applications in various fields and there are recommended books and online resources for studying it. A strong foundation in abstract algebra and linear algebra is recommended before delving into the subject.
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Tibarn
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I was wondering if anyone knows a decent list of books to prepare for and learn algebraic geometry. Rigor isn't a problem. As for my current preparation, I'm fairly comfortable with single-variable complex analysis and I'm currently making my way through Hungerford's "Algebra". Any help would be appreciated.
 
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I would recommend starting with "Algebraic Geometry" by Robin Hartshorne. This book provides a comprehensive introduction to the subject and covers both classical and modern approaches. Other highly regarded books include "Introduction to Algebraic Geometry" by Serge Lang and "Principles of Algebraic Geometry" by Phillip Griffiths and Joseph Harris. Additionally, for a more rigorous approach, "Algebraic Geometry: A First Course" by Joe Harris is a great resource. It is important to also supplement your learning with problem sets and exercises to solidify your understanding. Good luck with your studies!
 

1. What is algebraic geometry?

Algebraic geometry is a branch of mathematics that studies the solutions to systems of polynomial equations. It uses the tools of algebra to study the geometric properties of these solutions.

2. Why is algebraic geometry important?

Algebraic geometry has applications in many areas of mathematics, including number theory, topology, and differential geometry. It is also used in fields such as physics, engineering, and computer science.

3. What are some recommended books for learning algebraic geometry?

Some popular books for learning algebraic geometry include "Algebraic Geometry: A Problem Solving Approach" by Thomas Garrity, "Principles of Algebraic Geometry" by Phillip Griffiths and Joseph Harris, and "Algebraic Geometry" by Robin Hartshorne.

4. How should I prepare for studying algebraic geometry?

It is recommended to have a strong foundation in abstract algebra and linear algebra before studying algebraic geometry. Familiarity with basic concepts in topology and analysis can also be helpful.

5. Are there any online resources for studying algebraic geometry?

Yes, there are many online resources available for studying algebraic geometry, such as lecture notes, video lectures, and problem sets. Some popular websites for algebraic geometry include the Algebraic Geometry section on MathOverflow and the Algebraic Geometry section on StackExchange.

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