Algebraic Geometry

  1. Rational Maps and Birational Geometry
    1. Rational Maps
      1. Definition and Domain of Definition
        1. Indeterminacy Locus
          1. Composition of Rational Maps
          2. Birational Maps
            1. Definition and Examples
              1. Birational Equivalence
                1. Rational Function Fields
                2. Birational Invariants
                  1. Dimension
                    1. Function Field
                      1. Other Invariants
                      2. Blowing Up
                        1. Motivation and Geometric Interpretation
                          1. Blowing Up Points
                            1. Construction in Affine Space
                              1. Construction in Projective Space
                                1. Properties of Blow-up
                                2. Blowing Up Subvarieties
                                  1. General Construction
                                    1. Examples and Applications
                                    2. Resolution of Singularities
                                      1. Basic Concepts

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                                  5. Projective Algebraic Geometry

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                                  7. Local Properties and Singularities