--- _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 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. Bulletin of the London Mathematical Society. 2021;53(2):560-574. doi:10.1112/blms.12442 apa: Rychlewicz, K. P. (2021). The positivity of local equivariant Hirzebruch class for toric varieties. Bulletin of the London Mathematical Society. Wiley. https://doi.org/10.1112/blms.12442 chicago: Rychlewicz, Kamil P. “The Positivity of Local Equivariant Hirzebruch Class for Toric Varieties.” Bulletin of the London Mathematical Society. Wiley, 2021. https://doi.org/10.1112/blms.12442. ieee: K. P. Rychlewicz, “The positivity of local equivariant Hirzebruch class for toric varieties,” Bulletin of the London Mathematical Society, 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.” Bulletin of the London Mathematical Society, vol. 53, no. 2, Wiley, 2021, pp. 560–74, doi:10.1112/blms.12442. 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' ...