아핀다양체
Affine varieties and their basic properties
대수기하학
사영다양체
Projective varieties and homogeneous coordinates
준사영다양체
Quasi-projective varieties and regular maps
유리사상
Rational maps and birational equivalence
차원
Dimension of algebraic varieties
접공간과 매끄러움
Tangent spaces and smoothness of algebraic varieties
그라스만 다양체
Grassmannians as parameter spaces of linear subspaces
인자
Weil divisors, Cartier divisors, and divisor class groups
선다발과 벡터다발
Line bundles, invertible sheaves, and the Picard group
선형계
Complete linear systems, base loci, and ampleness