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Record Nr. |
UNINA9910828909403321 |
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Autore |
Fulton William |
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Titolo |
Intersection Theory / / by William Fulton |
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Pubbl/distr/stampa |
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New York, NY : , : Springer New York : , : Imprint : Springer, , 1998 |
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ISBN |
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Edizione |
[2nd ed. 1998.] |
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Descrizione fisica |
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1 online resource (XIII, 470 p.) |
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Collana |
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Ergebnisse der Mathematik und ihrer Grenzgebiete, , 0071-1136 ; ; Dritte Folge, volume 2 |
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Disciplina |
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Soggetti |
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Algebraic geometry |
Algebraic Geometry |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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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. |
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Sommario/riassunto |
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From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this 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 intersection theory. A suggested prerequisite 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 complete modern treatise of the subject and received the Steele Prize for best exposition in August 1996. |
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