William Fulton

Intersection Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

The aim of this book is to develop the foundations of intersection theory, and to indicate the range of classical and modern applications. Although a comprehensive history of this vast subject is not attempted, the author points out some of the striking early appearances of the ideas of this theory. A suggested prerequiste for the reading of this book is a first course in algebraic geometry. Fulton's introduction to intersection theory has been well used for more than 10 years. It is still the only existing comprehensive treatise of the subject and received the Steele Prize for best exposition in 1996.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 470
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461217008
• Artikelnr.: 44178737

Inhaltsangabe

Rational Equivalence.- Divisors.- Vector Bundles.- Cones and Segre Classes.- Deformations to the Normal Cone.- Intersection Products.- Intersection Multiplicites.- Intersections on Non-singular Varieties.- Excess and Residual Intersections.- Families of Algebraic Cycles.- Dynamic Intersections.- Positivity.- Rationality.- Degeneracy Loci and Grassmannians.- Riemann-Roch for Non-singular Varieties.- Correspondences.- Bivariant Intersections Theory.- Riemann-Roch for Singular Varieties.- Algebraic: Homological and Numerical Equivalence.- Generalizations. 1. 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.

Rezensionen

Review 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