Description
Book Synopsis1. Rational Equivalence.- 2. Divisors.- 3. Vector Bundles and Chern Classes.- 4. Cones and Segre Classes.- 5. Deformation to the Normal Cone.- 6. Intersection Products.- 7. Intersection Multiplicities.- 8. Intersections on Non-singular Varieties.- 9. Excess and Residual Intersections.- 10. Families of Algebraic Cycles.- 11. Dynamic Intersections.- 12. Positivity.- 13. Rationality.- 14. Degeneracy Loci and Grassmannians.- 15. Riemann-Roch for Non-singular Varieties.- 16. Correspondences.- 17. Bivariant Intersection Theory.- 18. Riemann-Roch for Singular Varieties.- 19. Algebraic, Homological and Numerical Equivalence.- 20. Generalizations.- Appendix A. Algebra.- Appendix B. Algebraic Geometry (Glossary).- Notation.
Trade ReviewReview of 1st Edition "...This text, with its brilliant content and excellently arranged, is a prime mover in algebraic geometry, and a must for each algebraic geometer! It is an indispensable reference book, an outstanding textbook, and a great source for geometric research in the future." -- MATHEMATICAL REVIEWS
Table of Contents1. Rational Equivalence.- 2. Divisors.- 3. Vector Bundles and Chern Classes.- 4. Cones and Segre Classes.- 5. Deformation to the Normal Cone.- 6. Intersection Products.- 7. Intersection Multiplicities.- 8. Intersections on Non-singular Varieties.- 9. Excess and Residual Intersections.- 10. Families of Algebraic Cycles.- 11. Dynamic Intersections.- 12. Positivity.- 13. Rationality.- 14. Degeneracy Loci and Grassmannians.- 15. Riemann-Roch for Non-singular Varieties.- 16. Correspondences.- 17. Bivariant Intersection Theory.- 18. Riemann-Roch for Singular Varieties.- 19. Algebraic, Homological and Numerical Equivalence.- 20. Generalizations.- Appendix A. Algebra.- Appendix B. Algebraic Geometry (Glossary).- Notation.
