%0 Journal Article %T Complex Cobordism of quasitoric orbifolds %A Soumen Sarkar %J Mathematics %D 2014 %I arXiv %R 10.1016/j.topol.2015.08.020 %X We construct manifolds and orbifolds with quasitoric boundary. We show that these manifolds and orbifolds with boundary has a stable complex structure. These induce explicit (orbifold) complex cobordism relations among quasitoric manifolds and orbifolds. In particular, we show that a quasitoric orbifold is complex cobordant to some copies of fake weighted projective spaces. The famous problem of Hirzebruch is that which complex cobordism classes in $\Omega^U$ contain connected nonsingular algebraic varieties? We give some sufficient conditions to show when a complex cobordism class may contains an almost complex quasitoric manifold. Andrew Wilfong give some necessary condition of this problem up to dimension 8. %U http://arxiv.org/abs/1406.1914v2