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arXiv · 2007.11537

The Brasselet-Sch\"urmann-Yokura conjecture on $L$-classes of singular varieties

J. Fernández de Bobadilla·I. Pallarés
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Abstract

In 2010, Brasselet, Sch\"urmann 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.

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BibTeXRIS

J. Fernández de Bobadilla, I. Pallarés. 2020-07-22. The Brasselet-Sch\"urmann-Yokura conjecture on $L$-classes of singular varieties. https://arxiv.org/abs/2007.11537

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