The Brasselet–Schürmann–Yokura Conjecture on L-Classes of Projective Rational Homology Manifolds.

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 that we find of independent interest. [ABSTRACT FROM AUTHOR]