  We consider a gas of N(=6, 10, 15) Bose particles with hard-core repulsion,
contained in a quasi-2D harmonic trap and subjected to an overall angular
velocity $\Omega$ about the z-axis. Exact diagonalization of the $n\times n$
many-body Hamiltonian matrix in given subspaces of the total (quantized)
angular momentum L$_{z}$, with $n\sim 10^{5}$(e.g. for L$_{z}$=N=15, n =240782)
was carried out using Davidson's algorithm. The many-body variational ground
state wavefunction, as also the corresponding energy and the reduced
one-particle density-matrix were calculated. With the usual identification of
$\Omega$ as the Lagrange multiplier associated with L$_{z}$ for a rotating
system, the $L_{z}-\Omega$ phase diagram (or the stability line) was determined
that gave a number of critical angular velocities $\Omega_{{\bf c}i},
i=1,2,3,... ,$ at which the ground state angular momentum and the associated
condensate fraction undergo abrupt jumps.
  A number of (total) angular momentum states were found to be stable at
successively higher critical angular velocities $\Omega_{{\bf c}i}, \
i=1,2,3,...$ for a given N. For $L_{z}>N$, the condensate was strongly
depleted. The critical $\Omega_{{\bf c}i}$ values, however, decreased with
increasing interaction strength as well as the particle number, and were
systematically greater than the non-variational Yrast-state values for the
single vortex state with L$_{z}$ =N. We have also observed that the condensate
fraction for the single vortex state (as also for the higher vortex states) did
not change significantly even as the 2-body interaction strength was varied
over several $(\sim 4)$ orders of magnitude in the moderately to the weakly
interacting regime.
