아핀다양체
Affine varieties and their basic properties
대수다양체
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
표준선다발
Canonical bundle and canonical divisor
층 코호몰로지
Sheaf cohomology and its applications
사영공간의 코호몰로지
Bott’s formula and the cohomology of line bundles on projective space
세르 쌍대성
Serre duality theorem and its applications
곡선에서의 리만-로흐 정리
The Riemann–Roch theorem for curves
곡면에서의 리만-로흐 정리
Intersection theory on surfaces and its applications
고다이라 소멸정리
Kodaira vanishing theorem과 그 응용
저우 군
Chow groups and the cycle class map
교차곱
The intersection product on Chow groups
베주 정리
Bézout’s theorem and its applications