Using density functional theory and statistical thermodynamics, we obtained the phase diagram of thin VnOm films of varying thickness (approximately 2-6 A, 1-6 vanadium layers) supported on alpha-Al2O3(0001). Depending on the temperature, oxygen pressure, and vanadium concentration, films with different thickness and termination may form. In ultrahigh vacuum (UHV), at room temperature and for low vanadium concentrations, an ultrathin (1 x 1) O=V-terminated film is most stable. As more vanadium is supplied, the thickest possible films form. Their structures and terminations correspond to previous findings for the (0001) surface of bulk V2O3 [Kresse et al., Surf. Sci. 2004, 555, 118]. The presence of surface vanadyl (O=V) groups is a prevalent feature. They are stable up to at least 800 K in UHV. Vanadyl oxygen atoms induce a V(2p) core-level shift of about 2 eV on the surface V atoms. The reducibility of the supported films is characterized by the energy of oxygen defect formation. For the stable structures, the results vary between 4.11 and 3.59 eV per 1/2O2. In contrast, oxygen removal from the V2O5(001) surface is much easier (1.93 eV). This provides a possible explanation for the lower catalytic activity of vanadium oxides supported on alumina compared to that of crystalline vanadia particles.