Real Algebraic Varieties. 1st ed. 2020

種類:

電子ブック

責任表示:

by Frédéric Mangolte

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Mangolte, Frédéric.
• SpringerLink (Online service)

シリーズ名:

Springer Monographs in Mathematics ;

ISBN:

9783030431044 [3030431045]    

注記:

Preface -- Introduction, Algebraic models of smooth manifolds -- 1. Algebraic varieties -- 2. R-varieties -- 3. Topology of varieties with an involution -- 4. Surfaces -- 5. Algebraic approximation -- 6. Three dimensional varieties -- Appendices -- Bibliography -- Glossary of Notations -- Index -- List of Examples -- List of Figures.
This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous. They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last tw

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