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100   $a20210219d2020      uy             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aReal algebraic varieties /$fFre?de?ric Mangolte
205   $a1st ed. 2020.
210  1$aCham, Switzerland :$cSpringer,$d[2020]
210  4$d©2020
215   $a1 online resource (XVIII, 444 p. 60 illus., 28 illus. in color.) 
225 1 $aSpringer Monographs in Mathematics,$x1439-7382
311   $a3-030-43103-7 
327   $aPreface -- 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.
330   $aThis book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous. They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the ?folklore?. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter. .
410  0$aSpringer Monographs in Mathematics,$x1439-7382
606   $aGeometry, Algebraic
615  0$aGeometry, Algebraic.
676   $a516.35
700   $aMangolte$b Fre?de?ric$01012546
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996418255703316
996   $aVariétés algébriques réelles$92907056
997   $aUNISA