Eisenbud and Harris - 3264 and All That

(unpublished draft)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 =

Section 1.1: The Chow Groups and their Ring Structure

 * 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 1.6: Exercises
= Chapter 2. Introductions to Grassmannians and Lines in $$\mathbb{P}^n$$ =

= Chapter 3. Introduction to Grassmannians in General =

= Chapter 4. Chow Groups =

= Chapter 5. Intersection Products and Pullbacks =

= Chapter 6. Interlude: Vector Bundles and Direct Images =

= Chapter 7. Vector Bundles and Chern Classes =

= Chapter 8. Lines on Hypersurfaces =

= Chapter 9. Singular Elements of Linear Series =

= Chapter 10. Compactifying Parameter Spaces =

= Chapter 11. Projective Bundles and their Chow Rings =

= Chapter 12. Segre Classes and Varieties of Linear Spaces =

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

= Chapter 14. Porteous's Formula =

= Chapter 15. Excess Intersections and Blowups =

= Chapter 16. The Grothendieck-Riemann-Roch Theorem =

= Chapter 17. Brill-Noether =

= Chapter 18. Appendix: Other Cycle Theories =

= Chapter 19. Appendix: Lefschetz Hyperplane Theorem and Applications =

= Chapter 20. Solutions to Selected Exercises =