Advanced Lectures in Mathematics

Algebraic Geometry

Part I: Schemes. With Examples and Exercises

Authors: Görtz, Ulrich, Wedhorn, Torsten

  • Der Wegbegleiter in das Feld der modernen algebraischen Geometrie im Bachelor/Master Studium

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About this Textbook

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 startet, 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.

Prevarieties - Spectrum of a Ring - Schemes - Fiber products - Schemes over fields - Local properties of schemes - Quasi-coherent modules - Representable functors - Separated morphisms - Finiteness Conditions - Vector bundles - Affine and proper morphisms - Projective morphisms - Flat morphisms and dimension - One-dimensional schemes - Examples

Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen
Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn

About the authors

Prof. Dr. Ulrich Görtz, Institut für Experimentelle Mathematik, Universität Duisburg-Essen.Essen.
Prof. Dr. Torsten Wedhorn, Institut für Mathematik, Universität Paderborn.

Prof. Dr. Ulrich Görtz, Institute of Experimental Mathematics, University Duisburg-Essen.
Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn.

Table of contents (17 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-8348-9722-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-8348-0676-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Geometry
Book Subtitle
Part I: Schemes. With Examples and Exercises
Authors
Series Title
Advanced Lectures in Mathematics
Copyright
2010
Publisher
Vieweg+Teubner Verlag
Copyright Holder
Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH, Wiesbaden
eBook ISBN
978-3-8348-9722-0
DOI
10.1007/978-3-8348-9722-0
Softcover ISBN
978-3-8348-0676-5
Series ISSN
0932-7134
Edition Number
1
Number of Pages
IV, 615
Topics