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Smith-Thom's inequality tells us that the sum of Betti numbers of the real locus of a
real algebraic variety is always smaller than or equal to the sum of Betti numbers of
its complex locus. In the case of equality, the real algebraic variety is called
maximal. Given a real holomorphic line bundle L over a real algebraic variety X, I
will prove that the probability that a real holomorphic section of L^d defines a
maximal hypersurface tends to 0 exponentially fast when d tends to infinity.
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