English

Todd genera of complex torus manifolds

Algebraic Topology 2014-10-01 v2

Abstract

In this paper, we prove that the Todd genus of a compact complex manifold XX of complex dimension nn with vanishing odd degree cohomology is one if the automorphism group of XX contains a compact nn-dimensional torus \Tn\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-Panov.

Keywords

Cite

@article{arxiv.1203.3129,
  title  = {Todd genera of complex torus manifolds},
  author = {Hiroaki Ishida and Mikiya Masuda},
  journal= {arXiv preprint arXiv:1203.3129},
  year   = {2014}
}

Comments

12 pages, Remark 1.2 is added

R2 v1 2026-06-21T20:34:00.543Z