Algebraic & Geometric Topology 12 (2012) 1777–1788

DOI: 10.2140/agt.2012.12.1777

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 Tⁿ 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

Primary: 57R91

Secondary: 32M05, 57S25

References

Publication

Received: 14 March 2012
Accepted: 21 June 2012
Published: 24 August 2012

Authors