article
On the Betti numbers of real varieties
Proceedings of the American Mathematical Society · 1964 · Vol. 15(2) · pp. 275–280
Abstract
PROOF. Approximate fi, * *, fm by real polynomials F1, * , Fm of the same degrees whose coefficients are algebraically independent. Now consider the variety Vc in the complex Cartesian space C'defined by the equations F1 =0, * * *, Fm =0. It follows from van der Waerden [9, ?41 ] that the number of points in Vc is equal to (deg fi) (deg f2) . . (deg fm). Since each point of V0 lies close to some real point of Vc; this proves Lemma 1.
Polynomial and algebraic computationAdvanced Numerical Analysis TechniquesAdvanced Differential Equations and Dynamical SystemsBetti numberMathematicsCombinatorics
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