Support curve Wikipedia
Support curve is a statistical term, coined by A. W. F. Edwards, to describe the graph of the natural logarithm of the likelihood function. It has a relation to, but is distinct from the support of a distribution.
The function being plotted is used in the computation of the score and Fisher information, and the graph has a direct interpretation in the context of maximum likelihood estimation and likelihood-ratio tests.
The term refers to the hypotheses being tested, i.e. whether or not the data support one hypothesis (or parameter value) more than any other.