  We theoretically analyze some of the anomalies of the optical sumrules in the
high-temperature superconductors. In particular we address the particularly
strong dependence on temperature of the sumrule in the normal state. Both
electron-electron correlations and the presence of a Van-Hove singularity have
been shown to enhance such a dependence. Here we consider both effects
simultaneously by means of Dynamical Mean-Field Theory for a two dimensional
Hubbard model with realistic parameters for different cuprates, and we find
that the two effects are not cooperative, as they appear to compete one another
in the region of parameters relevant for the experiments.
