We construct a new family of toric manifolds generating the unitary bordism ring. Each manifold in the family is the complex projectivisation of the sum of a line bundle and a trivial bundle over a complex projective space. We also construct a family of special unitary quasitoric manifolds which contains polynomial generators of the special unitary bordism ring with 2 inverted in dimensions . Each manifold in the latter family is obtained from an iterated complex projectivisation of a sum of line bundles by amending the complex structure to make the first Chern class vanish.
"On toric generators in the unitary and special unitary bordism rings." Algebr. Geom. Topol. 16 (5) 2865 - 2893, 2016. https://doi.org/10.2140/agt.2016.16.2865