The Brasselet-Schürmann-Yokura conjecture on $L$-classes of singular varieties
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866911801672728576 |
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| author | de Bobadilla, J. Fernández Pallarés, I. |
| author_facet | de Bobadilla, J. Fernández Pallarés, I. |
| contents | In 2010, Brasselet, Schürmann and Yokura conjectured an equality of characteristic classes of singular varieties between the Goresky-MacPherson $L$-class $L_*(X)$ and the Hirzebruch homology class $T_{1*}(X)$ for a compact complex algebraic variety $X$ that is a rational homology manifold. In this note we give a proof of this conjecture for projective varieties based on cubical hyperresolutions, the Decomposition Theorem, and Hodge theory. The crucial step of the proof is a new characterization of rational homology manifolds in terms of cubical hyperresolutions which we find of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2007_11537 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Brasselet-Schürmann-Yokura conjecture on $L$-classes of singular varieties de Bobadilla, J. Fernández Pallarés, I. Algebraic Geometry Algebraic Topology In 2010, Brasselet, Schürmann and Yokura conjectured an equality of characteristic classes of singular varieties between the Goresky-MacPherson $L$-class $L_*(X)$ and the Hirzebruch homology class $T_{1*}(X)$ for a compact complex algebraic variety $X$ that is a rational homology manifold. In this note we give a proof of this conjecture for projective varieties based on cubical hyperresolutions, the Decomposition Theorem, and Hodge theory. The crucial step of the proof is a new characterization of rational homology manifolds in terms of cubical hyperresolutions which we find of independent interest. |
| title | The Brasselet-Schürmann-Yokura conjecture on $L$-classes of singular varieties |
| topic | Algebraic Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2007.11537 |