  We consider the plasmonic eigenvalue problem for a general 2D domain with a
curvilinear corner, studying the spectral theory of the Neumann--Poincar\'e
operator of the boundary. A limiting absorption principle is proved, valid when
the spectral parameter approaches the essential spectrum. Putting the principle
into use, it is proved that the corner produces absolutely continuous spectrum
of multiplicity 1. The embedded eigenvalues are discrete. In particular, there
is no singular continuous spectrum.
