On the Betti numbers of real varieties

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.

Locations

• Proceedings of the American Mathematical Society - View - PDF
• CiteSeer X (The Pennsylvania State University) - View - PDF