Algebraic Geometry I: Schemes: With Examples and Exercises

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.

Author:

Ulrich G?rtz, Torsten Wedhorn

Publisher:

Springer Spektrum

Publication Date:

Oct 12, 2020

Number of pages:

633 pages

Language:

English

Binding:

Paperback

ISBN-10:

3658307323

ISBN-13:

9783658307325