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Algebraisk geometri

Format: Häftad (Paperback / softback)
Språk: Tyska
Antal sidor: 626
Utgivningsdatum: 2020-07-28
Upplaga: 2nd corr. ed. 2020
Förlag: Springer Spektrum
Originalspråk: German
Medarbetare: Wedhorn, Torsten
Illustrationer: 15 Illustrations, black and white; VII, 626 p. 15 illus.
Dimensioner: 244 x 170 x 33 mm
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Antal komponenter: 1
Komponenter: 1 Paperback / softback
ISBN: 9783658307325

Algebraic Geometry I: Schemes

Name: Algebraic Geometry I: Schemes
Price: 952.00 SEK
Availability: InStock
Author: Ulrich Grtz, Torsten Wedhorn
ISBN: 9783658307325

With Examples and Exercises

av Ulrich Grtz, Torsten Wedhorn

Häftad, Tyska, 2020-07-28

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This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get started, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes. For the second edition, several mistakes and many smaller errors and misprints have been corrected.

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Algebraic Geometry II: Cohomology of Schemes

Ulrich Grtz, Torsten Wedhorn

This book completes the comprehensive introduction to modern algebraic geometry which was started with the introductory volume Algebraic Geometry I: Schemes. It begins by discussing in detail the notions of smooth, unramified and tale morphisms in...

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Manifolds, Sheaves, and Cohomology

Torsten Wedhorn

This book explains techniques that are essential in almost all branches of modern geometry such as algebraic geometry, complex geometry, or non-archimedian geometry. It uses the most accessible case, real and complex manifolds, as a model. The aut...

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Prof. Dr. Ulrich Grtz, Institute of Experimental Mathematics, University Duisburg-Essen Prof. Dr. Torsten Wedhorn, Department of Mathematics, Technical University of Darmstadt

Introduction.- 1 Prevarieties.- 2 Spectrum of a Ring.- 3 Schemes.- 4 Fiber products.- 5 Schemes over fields.- 6 Local Properties of Schemes.- 7 Quasi-coherent modules.- 8 Representable Functors.- 9 Separated morphisms.- 10 Finiteness Conditions.- 11 Vector bundles.- 12 Affine and proper morphisms.- 13 Projective morphisms.- 14 Flat morphisms and dimension.- 15 One-dimensional schemes.- 16 Examples.