  Fact-checking requires retrieving evidence related to a claim under
investigation. The task can be formulated as question generation based on a
claim, followed by question answering. However, recent question generation
approaches assume that the answer is known and typically contained in a passage
given as input, whereas such passages are what is being sought when verifying a
claim. In this paper, we present {\it Varifocal}, a method that generates
questions based on different focal points within a given claim, i.e.\ different
spans of the claim and its metadata, such as its source and date. Our method
outperforms previous work on a fact-checking question generation dataset on a
wide range of automatic evaluation metrics. These results are corroborated by
our manual evaluation, which indicates that our method generates more relevant
and informative questions. We further demonstrate the potential of focal points
in generating sets of clarification questions for product descriptions.
