  Given an arithmetic surface and a positive hermitian line bundle over it, we
bound the successive minima of the lattice of global sections of this line
bundle.
  Our method combines a result of C.Voisin on secant varieties of projective
curves with previous work by the author on the arithmetic analog of the Kodaira
vanishing theorem. The paper also includes a result of A.Granville on the
divisibility properties of binomial coefficients in a given line of Pascal's
triangle.
