@article{10902/35896,
year = {2025},
url = {https://hdl.handle.net/10902/35896},
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.},
organization = {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.},
publisher = {European Mathematical Society Publishing House},
publisher = {Journal of the European Mathematical Society, 2025, 27(2), 773-800},
title = {Hodge modules and cobordism classes},
author = {Fernández de Bobadilla, Javier and Pallarés Torres, Irma and Saito, Morihiko},
}