The positivity of local equivariant Hirzebruch class for toric varieties

K.P. Rychlewicz, Bulletin of the London Mathematical Society (2020).


Journal Article | Epub ahead of print | English

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Abstract
The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber.
Publishing Year
Date Published
2020-11-30
Journal Title
Bulletin of the London Mathematical Society
Article Number
12442
ISSN
eISSN
IST-REx-ID

Cite this

Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. 2020. doi:10.1112/blms.12442
Rychlewicz, K. P. (2020). The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. Wiley. https://doi.org/10.1112/blms.12442
Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” Bulletin of the London Mathematical Society. Wiley, 2020. https://doi.org/10.1112/blms.12442.
K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for toric varieties,” Bulletin of the London Mathematical Society. Wiley, 2020.
Rychlewicz KP. 2020. The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society., 12442.
Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” Bulletin of the London Mathematical Society, 12442, Wiley, 2020, doi:10.1112/blms.12442.
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