---
_id: '6965'
abstract:
- lang: eng
  text: 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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Kamil P
  full_name: Rychlewicz, Kamil P
  id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
  last_name: Rychlewicz
citation:
  ama: Rychlewicz KP. The positivity of local equivariant Hirzebruch class for toric
    varieties. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):560-574.
    doi:<a href="https://doi.org/10.1112/blms.12442">10.1112/blms.12442</a>
  apa: Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class
    for toric varieties. <i>Bulletin of the London Mathematical Society</i>. Wiley.
    <a href="https://doi.org/10.1112/blms.12442">https://doi.org/10.1112/blms.12442</a>
  chicago: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
    for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>. Wiley,
    2021. <a href="https://doi.org/10.1112/blms.12442">https://doi.org/10.1112/blms.12442</a>.
  ieee: K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for
    toric varieties,” <i>Bulletin of the London Mathematical Society</i>, vol. 53,
    no. 2. Wiley, pp. 560–574, 2021.
  ista: Rychlewicz KP. 2021. The positivity of local equivariant Hirzebruch class
    for toric varieties. Bulletin of the London Mathematical Society. 53(2), 560–574.
  mla: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class
    for Toric Varieties.” <i>Bulletin of the London Mathematical Society</i>, vol.
    53, no. 2, Wiley, 2021, pp. 560–74, doi:<a href="https://doi.org/10.1112/blms.12442">10.1112/blms.12442</a>.
  short: K.P. Rychlewicz, Bulletin of the London Mathematical Society 53 (2021) 560–574.
date_created: 2019-10-24T08:04:09Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-08-04T10:43:39Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/blms.12442
external_id:
  arxiv:
  - '1910.10435'
  isi:
  - '000594805800001'
intvolume: '        53'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.10435
month: '04'
oa: 1
oa_version: Preprint
page: 560-574
publication: Bulletin of the London Mathematical Society
publication_identifier:
  eissn:
  - 1469-2120
  issn:
  - 0024-6093
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: The positivity of local equivariant Hirzebruch class for toric varieties
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2021'
...