Algebraic Geometry

Contents......Page Hartshorne0008_0001.djvu
Introduction......Page Hartshorne0012_0001.djvu
1. Affine Varieties......Page Hartshorne001_0001.djvu
2. Projective Varieties......Page Hartshorne008_0001.djvu
3. Morphisms......Page Hartshorne014_0001.djvu
4. Rational Maps......Page Hartshorne024_0001.djvu
5. Nonsingular Varieties......Page Hartshorne031_0001.djvu
6. Nonsingular Curves......Page Hartshorne039_0001.djvu
7. Intersections in Projective Space......Page Hartshorne047_0001.djvu
8. What Is Algebraic Geometry?......Page Hartshorne055_0001.djvu
1. Sheaves......Page Hartshorne060_0001.djvu
2. Schemes......Page Hartshorne069_0001.djvu
3. First Properties of Schemes......Page Hartshorne082_0001.djvu
4. Separated and Proper Morphisms......Page Hartshorne095_0001.djvu
5. Sheaves of Modules......Page Hartshorne108_0001.djvu
6. Divisors......Page Hartshorne129_0001.djvu
7. Projective Morphisms......Page Hartshorne149_0001.djvu
8. Differentials......Page Hartshorne172_0001.djvu
9. Formal Schemes......Page Hartshorne190_0001.djvu
III. Cohomology......Page Hartshorne201_0001.djvu
1. Derived Functors......Page Hartshorne202_0001.djvu
2. Cohomology of Sheaves......Page Hartshorne206_0001.djvu
3. Cohomology of a Noetherian Affine Scheme......Page Hartshorne213_0001.djvu
4. Cech Cohomology......Page Hartshorne218_0001.djvu
5. The Cohomology of Projective Space......Page Hartshorne225_0001.djvu
6. Ext Groups and Sheaves......Page Hartshorne233_0001.djvu
7. The Serre Duality Theorem......Page Hartshorne239_0001.djvu
8. Higher Direct Images of Sheaves......Page Hartshorne250_0001.djvu
9. Flat Morphisms......Page Hartshorne253_0001.djvu
10. Smooth Morphisms......Page Hartshorne268_0001.djvu
11. The Theorem on Formal Functions......Page Hartshorne276_0001.djvu
12. The Semicontinuity Theorem......Page Hartshorne281_0001.djvu
IV. Curves......Page Hartshorne293_0001.djvu
1. Riemann-Roch Theorem......Page Hartshorne294_0001.djvu
2. Hurwitz\'s Theorem......Page Hartshorne299_0001.djvu
3. Embeddings in Projective Space......Page Hartshorne307_0001.djvu
4. Elliptic Curves......Page Hartshorne316_0001.djvu
5. The Canonical Embedding......Page Hartshorne340_0001.djvu
6. Classification of Curves in P^3......Page Hartshorne349_0001.djvu
V. Surfaces......Page Hartshorne356_0001.djvu
1. Geometry on a Surface......Page Hartshorne357_0001.djvu
2. Ruled Surfaces......Page Hartshorne369_0001.djvu
3. Monoidal Transformations......Page Hartshorne386_0001.djvu
4. The Cubic Surface in P^3......Page Hartshorne391_0001.djvu
5. Birational Transformations......Page Hartshorne409_0001.djvu
6. Classification of Surfaces......Page Hartshorne421_0001.djvu
A. Intersection Theory......Page Hartshorne424_0001.djvu
1. Intersection Theory......Page Hartshorne425_0001.djvu
2. Properties of the Chow Ring......Page Hartshorne428_0001.djvu
3. Chern Classes......Page Hartshorne429_0001.djvu
4. The Riemann-Roch Theorem......Page Hartshorne431_0001.djvu
5. Complements and Generalizations......Page Hartshorne434_0001.djvu
1. The Associated Complex Analytic Space......Page Hartshorne438_0001.djvu
2. Comparison of the Algebraic and Analytic Categories......Page Hartshorne440_0001.djvu
3. When is a Compact Complex Manifold Algebraic?......Page Hartshorne441_0001.djvu
4. Kähler Manifolds......Page Hartshorne445_0001.djvu
5. The Exponential Sequence......Page Hartshorne446_0001.djvu
1. The Zeta Function and the Weil Conjectures......Page Hartshorne449_0001.djvu
2. History of Work on the Weil Conjectures......Page Hartshorne451_0001.djvu
3. The l-adic Cohomology......Page Hartshorne453_0001.djvu
4. Cohomological Interpretation of the Weil Conjectures......Page Hartshorne454_0001.djvu
Bibliography......Page Hartshorne459_0001.djvu
Results from Algebra......Page Hartshorne470_0001.djvu
Glossary of Notations......Page Hartshorne472_0001.djvu
Index......Page Hartshorne478_0001.djvu