  Motivated by the embedding problem of canonical models in small codimension,
we extend Severi's double point formula to the case of surfaces with rational
double points, and we give more general double point formulae for varieties
with isolated singularities.
  A concrete application is for surfaces with geometric genus $p_g=5$: the
canonical model is embedded in $\mathbb{P}^4$ if and only if we have a complete
intersection of type $(2,4)$ or $(3,3)$.
