  We investigate the asymmetry between electron and hole doping in a 2D Mott
insulator, and the resulting competition between antiferromagnetism (AF) and
d-wave superconductivity (SC), using variational Monte Carlo for projected wave
functions. We find that key features of the T = 0 phase diagram, such as
critical doping for SC-AF coexistence and the maximum value of the SC order
parameter, are determined by a single parameter which characterises the
topology of the "Fermi surface" at half filling defined by the bare
tight-binding parameters. Our results give insight into why AF wins for
electron doping, while SC is dominant on the hole doped side. We also suggest
using band structure engineering to control the parameter for enhancing SC.
