  We propose a model for high-T$_{c}$ superconductors, valid for
$0\leq\delta\leq\delta_{SC}$, that includes both the spin fluctuations of the
Cu$^{++}$ magnetic ions and of the O$^{--}$ doped holes. Spin-charge separation
is taken into account with the charge of the doped holes being associated to
quantum skyrmion excitations (holons) of the Cu$^{++}$ spin background. The
holon effective interaction potential is evaluated as a function of doping,
indicating that Cooper pair formation is determined by the competition between
the spin fluctuations of the Cu$^{++}$ background and of spins of the O$^{--}$
doped holes (spinons). The superconducting transition occurs when the spinon
fluctuations dominate, thereby reversing the sign of the interaction. At this
point ($\delta = \delta_{SC}$), the theory is supersymmetric at short distances
and, as a consequence, the leading order results are not modified by radiative
corrections. The critical doping parameter for the onset of superconductivity
at T=0 is obtained and found to be a universal constant determined by the shape
of the Fermi surface. Our theoretical values for $\delta_{SC}$ are in good
agreement with the experiment for both LSCO and YBCO.
