3264 and All That: A Second Course in Algebraic Geometry

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David Eisenbud (Professor, University of California, Berkeley) Joe Harris (Professor, Harvard University, Massachusetts)

3264 and All That

A Second Course in Algebraic Geometry

David Eisenbud (Professor, University of California, Berkeley), Joe Harris (Professor, Harvard University, Massachusetts)

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English

Cambridge University Press
14 April 2016

Algebraic geometry

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.

By: David Eisenbud (Professor University of California Berkeley), Joe Harris (Professor, Harvard University, Massachusetts)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 253mm, Width: 176mm, Spine: 35mm
Weight: 1.140kg
ISBN: 9781107602724
ISBN 10: 1107602726
Pages: 603
Publication Date: 14 April 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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.

Reviews for 3264 and All That: A Second Course in Algebraic Geometry

'… the book covers an important part of classical algebraic geometry with a modern point of view. It is indeed highly recommendable for a second (or a third) course in algebraic geometry| and more generally, for every mathematician interested in concrete algebraic geometry.' Arnaud Beauville, MathSciNet