  We investigated the ground state of spin-1 bosons interacting under local
two- and three-body interactions in one dimension by means of the density
matrix renormalization group method. We found that the even-odd asymmetry will
be obtained or not depending on the relative values of the two- and three-body
interactions. The Mott insulator lobes are spin isotropic, the first showing a
dimerized pattern and the second being composed of singlets. The three-body
interactions disfavor a longitudinal polar superfluid and a quantum phase
transition to a transverse polar superfluid occurs, which could be continuous
or discontinuous.
