Translator Disclaimer
2012 Todd genera of complex torus manifolds
Hiroaki Ishida, Mikiya Masuda
Algebr. Geom. Topol. 12(3): 1777-1788 (2012). 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.

Citation

Download Citation

Hiroaki Ishida. Mikiya Masuda. "Todd genera of complex torus manifolds." Algebr. Geom. Topol. 12 (3) 1777 - 1788, 2012. https://doi.org/10.2140/agt.2012.12.1777

Information

Received: 14 March 2012; Accepted: 21 June 2012; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1257.57035
MathSciNet: MR2979996
Digital Object Identifier: 10.2140/agt.2012.12.1777

Subjects:
Primary: 57R91
Secondary: 32M05, 57S25

Rights: Copyright © 2012 Mathematical Sciences Publishers

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.12 • No. 3 • 2012
MSP
Back to Top