3264 and All That - David Eisenbud, Joe Harris

3264 and All That

A Second Course in Algebraic Geometry
Buch | Hardcover
603 Seiten
2016
Cambridge University Press (Verlag)
978-1-107-01708-5 (ISBN)
114,70 inkl. MwSt
This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique so that the student develops the ability to solve geometric problems. It also contains abundant examples, exercises and solutions.
This book can form the basis of a second course in algebraic geometry. As motivation, it takes concrete questions from enumerative geometry and intersection theory, and provides intuition and technique, so that the student develops the ability to solve geometric problems. The authors explain key ideas, including rational equivalence, Chow rings, Schubert calculus and Chern classes, and readers will appreciate the abundant examples, many provided as exercises with solutions available online. Intersection is concerned with the enumeration of solutions of systems of polynomial equations in several variables. It has been an active area of mathematics since the work of Leibniz. Chasles' nineteenth-century calculation that there are 3264 smooth conic plane curves tangent to five given general conics was an important landmark, and was the inspiration behind the title of this book. Such computations were motivation for Poincaré's development of topology, and for many subsequent theories, so that intersection theory is now a central topic of modern mathematics.

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.

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.

Erscheinungsdatum
Zusatzinfo Worked examples or Exercises; 5 Halftones, black and white; 75 Line drawings, black and white
Verlagsort Cambridge
Sprache englisch
Maße 182 x 260 mm
Gewicht 1290 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-107-01708-4 / 1107017084
ISBN-13 978-1-107-01708-5 / 9781107017085
Zustand Neuware
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