  We have studied the variation of Tc with charge density and lattice
parameters in Mg1-xAlxB2 superconducting samples at low Al doping x<8%. We show
that high Tc occurs where the chemical potential is tuned at a "superconducting
shape resonance" near the energy Ec of the quantum critical point (QCP) for the
dimensional transition from 2D to 3D electronic structure in a particular
subband of the natural superlattice of metallic atomic boron layers. At the
"shape resonance" the electrons pairs see a 2D Fermi surface at EF-w0 and a 3D
Fermi surface at EF+wo, where wo is the energy cut off of the pairing
interaction. The resonant amplification occurs in a narrow energy range where
EF-Ec is in the range of 2wo.
