  We study spin-fluctuation-mediated superconductivity in the one-band Hubbard
model. Higher order effective interactions in $U$ give rise to a
superconducting instability which is very sensitive to changes in the Fermi
surface topology arising as a function of doping and changes in the band
structure. We show the superconducting phase diagram as a function of doping
and next-nearest neighbor hopping in the limit of very small Coulomb
interaction strength and discuss peculiarities arising at the phase boundaries
separating different superconducting domains.
