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.
About Ulrich Gortz
Prof. Dr. Ulrich Gortz, Institut fur Experimentelle Mathematik, Universitat DuisburgEssen.Essen. Prof. Dr. Torsten Wedhorn, Institut fur Mathematik, Universitat Paderborn. Prof. Dr. Ulrich Gortz, Institute of Experimental Mathematics, University DuisburgEssen. Prof. Dr. Torsten Wedhorn, Department of Mathematics, University of Paderborn.Details Book
Author  :  Ulrich Gortz 
Publisher  :  Vieweg Teubner Verlag 
Data Published  :  25 June 2010 
ISBN  :  3834806765 
EAN  :  9783834806765 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  615 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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