dc.contributor.author | Fernández de Bobadilla, Javier | |
dc.contributor.author | Pallarés Torres, Irma | |
dc.contributor.author | Saito, Morihiko | |
dc.contributor.other | Universidad de Cantabria | es_ES |
dc.date.accessioned | 2025-03-05T17:44:24Z | |
dc.date.available | 2025-03-05T17:44:24Z | |
dc.date.issued | 2025 | |
dc.identifier.issn | 1435-9855 | |
dc.identifier.issn | 1435-9863 | |
dc.identifier.other | MTM2016-76868-C2-1-P | es_ES |
dc.identifier.uri | https://hdl.handle.net/10902/35896 | |
dc.description.abstract | We show that the cobordism class of a polarization of Hodge module defines a natural transformation from the Grothendieck group of Hodge modules to the cobordism group of self-dual bounded complexes with real coefficients and constructible cohomology sheaves in a compatible way with push-forward by proper morphisms. This implies a new proof of the well-definedness of the natural transformation from the Grothendieck group of varieties over a given variety to the above cobordism group (with real coefficients). As a corollary, we get a slight extension of a conjecture of Brasselet, Schürmann and Yokura, showing that in the Q-homologically isolated singularity case, the homology L-class which is the specialization of the Hirzebruch class coincides with the intersection complex L-class defined by Goresky, MacPherson, and others if and only if the sum of the reduced modified Euler-Hodge signatures of the stalks of the shifted intersection complex vanishes. Here Hodge signature uses a polarization of Hodge structure, and it does not seem easy to define it by a purely topological method. | es_ES |
dc.description.sponsorship | g. J.F.B. was supported by ERCEA 615655 NMST Consolidator Grant, by MINECO through the project reference MTM2016-76868-C2-1-P (UCM), by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718, and by VIASM through a funded research visit. I.P. was supported by ERCEA 615655 NMST Consolidator Grant, by the Basque Government through the BERC 2018-2021 program and
Gobierno Vasco Grant IT1094-16, and by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718. M.S. was supported by JSPS Kakenhi 15K048. | es_ES |
dc.format.extent | 28 p. | es_ES |
dc.language.iso | eng | es_ES |
dc.publisher | European Mathematical Society Publishing House | es_ES |
dc.rights | Published by EMS Press and licensed under a CC BY 4.0 license | es_ES |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | * |
dc.source | Journal of the European Mathematical Society, 2025, 27(2), 773-800 | es_ES |
dc.subject.other | Characteristic classes for singular varieties | es_ES |
dc.subject.other | L-classes | es_ES |
dc.subject.other | Rational homology manifolds | es_ES |
dc.subject.other | Cobordism classes | es_ES |
dc.subject.other | Hodge modules | es_ES |
dc.title | Hodge modules and cobordism classes | es_ES |
dc.type | info:eu-repo/semantics/article | es_ES |
dc.relation.publisherVersion | https://doi.org/10.4171/jems/1387 | es_ES |
dc.rights.accessRights | openAccess | es_ES |
dc.identifier.DOI | 10.4171/JEMS/1387 | |
dc.type.version | publishedVersion | es_ES |