The Brasselet-Schürmann-Yokura conjecture on L-classes of singular varieties

2020/07/22 by de Bobadilla, J. Fernández, Pallarés, I.
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.11537

Abstract

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.

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