  The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic
and polar phases that combine magnetic and superfluid ordering. We analyze the
topological defects of the polar condensate, correcting previous studies, and
show that the polar condensate in two dimensions is unstable at any finite
temperature; instead there is a nematic or paired superfluid phase with
algebraic order in $\exp(2 i \theta)$, where $\theta$ is the superfluid phase,
and no magnetic order. The Kosterlitz-Thouless transition out of this phase is
driven by unbinding of half-vortices (the spin-disordered version of the
combined spin and phase defects found by Zhou), and the anomalous universal $8
T_c / \pi$ stiffness jump at the transition is confirmed in numerical
simulations. The anomalous stiffness jump is a clear experimental signature of
this phase and the corresponding phase transition.
