  We study a special kind of singular vorticities in ideal 2D fluids that
combine features of point vortices and vortex sheets, namely pointed vortex
loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism
group of ${\mathbb R}^2$ determined by them. We show that a polarization
subgroup consists of diffeomorphisms that preserve the loop as a set, thus the
configuration space is the space of loops that enclose a fixed area, without
information on vorticity distribution and attached points.
