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We study the expectation of the number of components b0(X) of a random algebraic hypersurface X defined by the zero set in projective space RPn of a random homogeneous polynomial f of degree d. Specifically, we consider invariant ensembles, that is Gaussian ensembles of polynomials that are invariant under an orthogonal change of variables.Fixing n, under some rescaling assumptions on the family of...
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