  The total curvature of complex hypersurfaces in $\bC^{n+1}$ and its variation
in families appear to depend not only on singularities but also on the
behaviour in the neighbourhood of infinity. We find the asymptotic loss of
total curvature towards infinity and we express the total curvature and the
Gauss-Bonnet defect in terms of singularities and tangencies at infinity.
