  Given a positive real Hermitian holomorphic line bundle L over a smooth real
projective manifold X, the space of real holomorphic sections of the bundle L^d
inherits for every positive integer d a L^2 scalar product which induces a
Gaussian measure. When X is a curve or a surface, we estimate the volume of the
cone of real sections whose vanishing locus contains many real components. In
particular, the volume of the cone of maximal real sections decreases
exponentially as d grows to infinity.
