We prove that the Todd genus of a compact complex manifold of complex dimension with vanishing odd degree cohomology is one if the automorphism group of contains a compact –dimensional torus as a subgroup. This implies that if a quasitoric manifold admits an invariant complex structure, then it is equivariantly homeomorphic to a compact smooth toric variety, which gives a negative answer to a problem posed by Buchstaber and Panov.
"Todd genera of complex torus manifolds." Algebr. Geom. Topol. 12 (3) 1777 - 1788, 2012. https://doi.org/10.2140/agt.2012.12.1777