#### Volume 12, issue 3 (2012)

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Todd genera of complex torus manifolds

### Hiroaki Ishida and Mikiya Masuda

Algebraic & Geometric Topology 12 (2012) 1777–1788
##### Abstract

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.

##### Keywords
Todd genera, quasitoric manifolds, torus manifolds, complex manifold, toric manifold
##### Mathematical Subject Classification 2010
Primary: 57R91
Secondary: 32M05, 57S25