Ankündigung Erscheint vsl. August 2020 Abbildung von Mangolte | Real Algebraic Varieties | 1st ed. 2020 | 2020


Real Algebraic Varieties

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Buch. Hardcover

1st ed. 2020. 2020

xix, 496 S.

Springer. ISBN 978-3-030-43103-7

Format (B x L): 15,5 x 23,5 cm

Das Werk ist Teil der Reihe: Springer Monographs in Mathematics


This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered during the 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 master 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 terms of topology and geometry of varieties of dimension two and three, without forgetting the curves, the central subject of Hilbert's famous sixteenth problem. Various level exercises are given, and the solutions of many of them are provided at the end of each chapter.


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