  Let K be a number field, O_K the ring of integers of K and X a stable curve
over O_K of genus g >= 2. In this note, we will prove a strict inequality
  ( (K_{X/S})^2 / [K : Q] ) > Height_{Fal}(J(X_K)),
  where $K_{X/S}$ is the canonically metrized dualizing sheaf of X over S =
Spec(O_K) and Height_{Fal}(J(X_K)) is the Faltings modular height of the
Jacobian of X_K. As corollary, for any constant A, the set of all stable curves
X over O_K with
  ( (K_{X/S})^2 / [K : Q] ) <= A
  is finite under the following equivalence. For stable curves X and Y, X is
equivalent to Y if X is isomorphic to Y over O_{K'} for some finite extension
field K' of K.
