Basic algebraic geometry

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1. johncarlosbaezOct 2025
   You need to go more slowly and do lots of examples. Maybe start with

   * Karen E. Smith, Lauri Kahanpää, Pekka Kekäläinen and William Traves, An Invitation to Algebraic Geometry, Springer, Berlin, 2004.

   and then this:

   * Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.

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2. johncarlosbaezMar 2019
   My favorite intros to algebraic geometry are these:

   Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.

   Phillip Griffiths and Joseph Harris, Principles of Algebraic Geometry, 1994. (Especially nice if you like complex analysis, differential geometry and de Rham theory.)

   David Eisenbud and Joseph Harris, The Geometry of Schemes, Springer, 2010. Currently at https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.p...

   But whenever I want to learn some new field of math I start with Wikipedia. This is a pretty good overview:

   https://en.wikipedia.org/wiki/Algebraic_geometry

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3. grnFeb 2011
   My favourites would be:

   - anything written by Serre,

   - Shafarevich's Basic Algebraic Geometry,

   - Silverman's The Artihmetic of Elliptic Curves,

   - Milne's notes (available at http://jmilne.org).

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