Real Algebraic Varieties - Frédéric Mangolte

Real Algebraic Varieties

Buch | Hardcover
XVIII, 444 Seiten
2020 | 1st ed. 2020
Springer International Publishing (Verlag)
978-3-030-43103-7 (ISBN)
128,39 inkl. MwSt

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 knowledgeis 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.


Frédéric Mangolte is Professor at Angers University in France. He is a specialist of real algebraic varieties, namely of their topology and their geometry. His research is focused on algebraic surfaces, algebraic threefolds and the Cremona group.

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

Erscheinungsdatum
Reihe/Serie Springer Monographs in Mathematics
Übersetzer Catriona Maclean
Zusatzinfo XVIII, 444 p. 60 illus., 28 illus. in color.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 857 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Geometrie / Topologie
Schlagworte algebraic cycle • Cremona group • Nash conjecture • real algebraic geometry • topology of algebraic varieties
ISBN-10 3-030-43103-7 / 3030431037
ISBN-13 978-3-030-43103-7 / 9783030431037
Zustand Neuware
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