Geodesic
Todd genera of complex torus manifolds
Ishida, Hiroaki1 ; Masuda, Mikiya2
1Osaka City University Advanced Mathematical Institute, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-shi 558-8585, Japan
2Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-shi 558-8585, Japan
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1777-1788
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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.

DOI : 10.2140/agt.2012.12.1777
Classification : 57R91, 32M05, 57S25
Keywords: Todd genera, quasitoric manifolds, torus manifolds, complex manifold, toric manifold

Ishida, Hiroaki  1   ; Masuda, Mikiya  2

1 Osaka City University Advanced Mathematical Institute, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-shi 558-8585, Japan
2 Department of Mathematics, Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka-shi 558-8585, Japan 
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Ishida, Hiroaki; Masuda, Mikiya. Todd genera of complex torus manifolds. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1777-1788. doi: 10.2140/agt.2012.12.1777

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