  Starting from the copper-oxygen Hamiltonian of the CuO2 planes, we derive
analytically an extended 1-band Hubbard Hamiltonian for the electrons on copper
sites, through a canonical transformation which eliminates the oxygen sites.
The model sustains a variety of phases : checkerboard states, stripes,
antiferromagnetism, local pairs and mixtures thereof. This approach may be
helpful in understanding what is so special about the CuO2 planes, as opposed
to other compounds.
