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 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 2010
Primary: 57R91
Secondary: 32M05, 57S25
References
Publication
Received: 14 March 2012
Accepted: 21 June 2012
Published: 24 August 2012
Authors
Hiroaki Ishida
Osaka City University Advanced Mathematical Institute
Osaka City University
3-3-138, Sugimoto, Sumiyoshi-ku
Osaka-shi 558-8585
Japan
Mikiya Masuda
Department of Mathematics
Osaka City University
3-3-138, Sugimoto, Sumiyoshi-ku
Osaka-shi 558-8585
Japan