On the pointwise supremum of the set of copulas with a given curvilinear section

Making use of the total variation of particular functions, we give an explicit formula for the pointwise supremum of the set of all copulas with a given curvilinear section. When the pointwise supremum is a copula is characterized. We also characterize the coincidence of the pointwise supremum and the greatest quasi-copula with the same curvilinear section.