Algebraic Geometry 1: Schemes. With Examples and Exercises - ISBN:3834806765

Algebraic Geometry 1: Schemes. With Examples and Exercises

Date: 21 April 2011, 04:08

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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. The two example classes of Hilbert modular surfaces and 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 book consists of an introductory volume on schemes and a second volume on the cohomology of schemes. The first volume requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix.

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