Author | Fulton, William. author |
---|---|

Title | Intersection Theory [electronic resource] / by William Fulton |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1984 |

Edition | 3. Folge |

Connect to | http://dx.doi.org/10.1007/978-3-662-02421-8 |

Descript | XI, 472 p. 3 illus. online resource |

SUMMARY

From the ancient origins of algebraic geometry in the solution of polynomial equations, through the triumphs of algebraic geometry during the last two cenยญ turies, intersection theory has played a central role. Since its role in foundaยญ tional crises has been no less prominent, the lack of a complete modern treatise on intersection theory has been something of an embarrassment. 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 hisยญ tory of this vast subject is not attempted, we have tried to point out some of the striking early appearances of the ideas of intersection theory. Recent improvements in our understanding not only yield a stronger and more useful theory than previously available, but also make it possible to develยญ op the subject from the beginning with fewer prerequisites from algebra and algebraic geometry. It is hoped that the basic text can be read by one equipped with a first course in algebraic geometry, with occasional use of the two appenยญ dices. Some of the examples, and a few of the later sections, require more speยญ cialized knowledge. The text is designed so that one who understands the conยญ structions and grants the main theorems of the first six chapters can read other chapters separately. Frequent parenthetical references to previous sections are included for such readers. The summaries which begin each chapter should faยญ cilitate use as a reference

CONTENT

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 -- Summary -- A.1 Length -- A.2 Herbrand Quotients -- A.3 Order Functions -- A.4 Flatness -- A.5 Koszul Complexes -- A.6 Regular Sequences -- A.7 Depth -- A.8 Normal Domains -- A.9 Determinantal Identities -- Notes and References -- Appendix B. Algebraic Geometry (Glossary) -- B.1 Algebraic Schemes -- B.2 Morphisms -- B.3 Vector Bundles -- B.4 Cartier Divisors -- B.5 Projective Cones and Bundles -- B.6 Normal Cones and Blowing Up -- B.7 Regular Imbeddings and l.c.i. Morphisms -- B.8 Bundles on Imbeddable Schemes -- B.9 General Position -- Notation

Mathematics
Algebraic geometry
Mathematics
Algebraic Geometry