The textbook "The Cambridge Grammar of the English Language", page 216:
We distinguish between core and non-core complements. Prototypically core complements have the form of NPs, non-core complements that of PPs.
The textbook "The Cambridge Grammar of the English Language", page 59:
Manner expressions, for example, are mostly adjuncts, but there are a few verbs that take manner complements: in "They treated us badly", the dependent "badly" counts as a complement by virtue of being obligatory (for "They treated us" involves a different sense of "treat").
Is the adverb "badly" in "They treat us badly" a core or non-core complement?