  We present ab-initio electronic structure calculations for the Si-terminated
SiC(0001)$\sqrt{3}\times\sqrt{3}$ surface. While local density approximation
(LDA) calculations predict a metallic ground state with a half-filled narrow
band, Coulomb effects, included by the spin-polarized LDA+U method, result in a
magnetic (Mott-Hubbard) insulator with a gap of 1.5 eV, comparable with the
experimental value of 2.0 eV. The calculated value of the inter-site exchange
parameter, J=30K, leads to the prediction of a paramagnetic Mott state, except
at very low temperatures. The observed Si 2p surface core level doublet can
naturally be explained as an on-site exchange splitting.
