  We study the Degrees of Freedom (DoF) of the K-user interference channel with
coordinated multi-point (CoMP) transmission and reception. Each message is
jointly transmitted by M_t successive transmitters, and is jointly received by
M_r successive receivers. We refer to this channel as the CoMP channel with a
transmit cooperation order of M_t and receive cooperation order of M_r. Since
the channel has a total of K transmit antennas and K receive antennas, the
maximum possible DoF is equal to K. We show that the CoMP channel has K DoF if
and only if M_t + M_r is greater than or equal to K+1. For the general case, we
derive an outer bound that states that the DoF is bounded above by the ceiling
of (K+M_t+M_r-2)/2. For the special case with only CoMP transmission, i.e, M_r
= 1, we propose a scheme that can achieve (K+M_t-1)/2 DoF for all K < 10, and
conjecture that the result holds true for all K . The achievability proofs are
based on the notion of algebraic independence from algebraic geometry.
