Robin Hartshorne

Algebraic Geometry

• Gebundenes Buch

Produktbeschreibung

An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra.Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

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Produktdetails

• Graduate Texts in Mathematics Nr.52
• Verlag: Springer New York / Springer US
• Artikelnr. des Verlages: 10187090
• 1977
• Seitenzahl: 516
• Erscheinungstermin: 19. Dezember 1977
• Englisch
• Abmessung: 241mm x 160mm x 34mm
• Gewicht: 934g
• ISBN-13: 9783540902447
• ISBN-10: 3540902449
• Artikelnr.: 21331485

Inhaltsangabe

I Varieties.- II Schemes.- III Cohomology.- IV Curves.- V Surfaces.- Appendix A Intersection Theory.- 1 Intersection Theory.- 2 Properties of the Chow Ring.- 3 Chern Classes.- 4 The Riemann-Roch Theorem.- 5 Complements and Generalizations.- Appendix B Transcendental Methods.- 1 The Associated Complex Analytic Space.- 2 Comparison of the Algebraic and Analytic Categories.- 3 When is a Compact Complex Manifold Algebraic?.- 4 Kähler Manifolds.- 5 The Exponential Sequence.- Appendix C The Weil Conjectures.- 1 The Zeta Function and the Weil Conjectures.- 2 History of Work on the Weil Conjectures.- 3 The /-adic Cohomology.- 4 Cohomological Interpretation of the Weil Conjectures.- Results from Algebra.- Glossary of Notations.

Rezensionen

"Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions." MATHEMATICAL REVIEWS

R. Hartshorne Algebraic Geometry "Enables the reader to make the drastic transition between the basic, intuitive questions about affine and projective varieties with which the subject begins, and the elaborate general methodology of schemes and cohomology employed currently to answer these questions."-MATHEMATICAL REVIEWS