Algebraic Geometry

  1. Divisors and Line Bundles
    1. Weil Divisors
      1. Definition on Normal Varieties
        1. Prime Divisors
          1. Divisor Group
            1. Principal Divisors
              1. Divisors of Rational Functions
              2. Linear Equivalence
                1. Divisor Class Group
                2. Cartier Divisors
                  1. Definition via Local Equations
                    1. Relationship to Weil Divisors
                      1. Principal Cartier Divisors
                        1. Cartier Divisor Group
                        2. Line Bundles and Invertible Sheaves
                          1. Definition of Line Bundles
                            1. Invertible Sheaves
                              1. Correspondence with Cartier Divisors
                                1. Picard Group
                                  1. Definition and Properties
                                    1. Relationship to Divisor Class Group
                                  2. Linear Systems
                                    1. Definition and Examples
                                      1. Complete Linear Systems
                                        1. Base Locus
                                          1. Dimension of Linear Systems
                                          2. Ample and Very Ample Divisors
                                            1. Definitions and Characterizations
                                              1. Projective Embeddings
                                                1. Embeddings via Very Ample Line Bundles
                                                2. Ampleness Criteria
                                                  1. Nakai-Moishezon Criterion
                                                    1. Kleiman's Criterion

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                                                9. Coherent Sheaves and Cohomology

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                                                11. Algebraic Curves