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(unpublished draft)

Algebraic Geometry

"Algebraic geometry is one of the central subjects of mathematics... and intersection theory is at the heart of algebraic geometry."

Chapter 1. Overture Edit

Section 1.1: The Chow Groups and their Ring Structure Edit

  • In the example showing that $ Div_0(\alpha) $ doesn't necessarily correspond to the divisor of the numerator of any representation of $ \alpha $, there is a small typo: M should be the line y = z = 0. Also, to calculate the divisor, note that on this cone x/y = y/z.

Section 1.2: Chow Ring Examples Edit

Section 1.3: The Canonical Class and the Adjunction Formula Edit

Section 1.4: Curves on surfaces Edit

Section 1.5: The idea of Chern Classes Edit

Section 1.6: Exercises Edit

Chapter 2. Introductions to Grassmannians and Lines in $ \mathbb{P}^n $ Edit

Chapter 3. Introduction to Grassmannians in General Edit

Chapter 4. Chow Groups Edit

Chapter 5. Intersection Products and Pullbacks Edit

Chapter 6. Interlude: Vector Bundles and Direct Images Edit

Chapter 7. Vector Bundles and Chern Classes Edit

Chapter 8. Lines on Hypersurfaces Edit

Chapter 9. Singular Elements of Linear Series Edit

Chapter 10. Compactifying Parameter Spaces Edit

Chapter 11. Projective Bundles and their Chow Rings Edit

Chapter 12. Segre Classes and Varieties of Linear Spaces Edit

Chapter 13. Contact Problems and Bundles of Relative Principal Parts Edit

Chapter 14. Porteous's Formula Edit

Chapter 15. Excess Intersections and Blowups Edit

Chapter 16. The Grothendieck-Riemann-Roch Theorem Edit

Chapter 17. Brill-Noether Edit

Chapter 18. Appendix: Other Cycle Theories Edit

Chapter 19. Appendix: Lefschetz Hyperplane Theorem and Applications Edit

Chapter 20. Solutions to Selected Exercises Edit