  The Cosmic Microwave Background (CMB) anisotropy constrains the geometry of
the Universe because the positions of the acoustic peaks of the angular power
spectrum depend strongly on the curvature of underlying three-dimensional
space. In this Letter we exploit current observations to determine the spatial
geometry of the Universe in the presence of isocurvature modes. Previous
analyses have always assumed that the cosmological perturbations were initially
adiabatic. A priori one might expect that allowing additional isocurvature
modes would substantially degrade the constraints on the curvature of the
Universe. We find, however, that if one considers additional data sets, the
geometry remains well constrained. When the most general isocurvature
perturbation is allowed, the CMB alone can only poorly constrain the geometry
to Omega_0=1.6+-0.3. Including large-scale structure (LSS) data one obtains
Omega_0=1.07+-0.03, and Omega_0=1.06+-0.02 when supplemented by the Hubble
Space Telescope (HST) Key Project determination of H_0 and SNIa data.
