  We consider families of Calabi-Yau n-folds containing singular fibres and
study relations between the occurring singularity structure and the
decomposition of the local Weil zeta-function. For 1-parameter families, this
provides new insights into the combinatorial structure of the strong
equivalence classes arising in the Candelas - de la Ossa - Rodrigues-Villegas
approach for computing the zeta-function. This can also be extended to families
with more parameters as is explored in several examples, where the singularity
analysis provides correct predictions for the changes of degree in the
decomposition of the zeta-function when passing to singular fibres. These
observations provide first evidence in higher dimensions for Lauder's
conjectured analogue of the Clemens-Schmid exact sequence.
