Todd genera of complex torus manifolds

Hiroaki Ishida, Mikiya Masuda
2012 Algebraic and Geometric Topology  
We prove that the Todd genus of a compact complex manifold X of complex dimension n with vanishing odd degree cohomology is one if the automorphism group of X contains a compact n-dimensional torus T n 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.
doi:10.2140/agt.2012.12.1781 fatcat:6jcpkztptrgo3nhwa7cpdwkguq