Elementary Structure of Real Algebraic Varieties
A real (or complex) algebraic variety V is a point set in real n-space R n (or complex n-space C n ) which is the set of common zeros of a set of polynomials. The general properties of a real V as a point set have not been the subject of much study recently (but see for instance ,  and ); attention has turned more to the complex case, the complex projective case, and especially the abstract algebraic theory. Facts about the real case are sometimes needed in the applications; proofs are commonly very difficult to locate.
KeywordsVariety Versus Algebraic Variety Constant Dimension Splitting Process Real Algebraic Variety
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