  We study the ground state of the rotating spinor condensate and show that for
slow rotation the ground state of the ferromagnetic spinor condensate is a
coreless vortex. While coreless vortex is not topologically stable, we show
that there is an energetic threshold for the creation of a coreless vortex.
This threshold corresponds to a critical rotation frequency that vanishes as
the system size increases. Also, we demonstrate the dramatically different
behavior of the spinor condensate with anti-ferromagnetic interactions. For
anti-ferromagnetic spinor condensate the angular momentum as a function of
rotation frequency exhibits the familiar staircase behavior, but in contrast to
an ordinary condensate the first step is to the state with angular momentum 1/2
per particle.
