Introduction; 1. Introducing the Chow ring; 2. First examples; 3. Introduction to Grassmannians and lines in P3; 4. Grassmannians in general; 5. Chern classes; 6. Lines on hypersurfaces; 7. Singular elements of linear series; 8. Compactifying parameter spaces; 9. Projective bundles and their Chow rings; 10. Segre classes and varieties of linear spaces; 11. Contact problems; 12. Porteous' formula; 13. Excess intersections and the Chow ring of a blow-up; 14. The Grothendieck-Riemann-Roch theorem; Appendix A. The moving lemma; Appendix B. Direct images, cohomology and base change; Appendix C. Topology of algebraic varieties; Appendix D. Maps from curves to projective space; References; Index.
Forming the basis of a second course in algebraic geometry, this book explains key ideas, each illustrated with abundant examples.
David Eisenbud is Professor of Mathematics at the University of California, Berkeley, and currently serves as Director of the Mathematical Sciences Research Institute. He is also a Director at Math for America, a foundation devoted to improving mathematics teaching. Joe Harris is Professor of Mathematics at Harvard University.
'... the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.' Arnaud Beauville, MathSciNet