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Real Algebraic Varieties (Paperback, 1st ed. 2020)
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Real Algebraic Varieties (Paperback, 1st ed. 2020)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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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
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.
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