论文标题
Brasselet-Schürmann-Yokura猜想在$ l $ - 单数品种的类别
The Brasselet-Schürmann-Yokura conjecture on $L$-classes of singular varieties
论文作者
论文摘要
在2010年，Brasselet，Schürmann和Yokura猜想了Goresky-Macpherson $ l $ -class $ -Class $ l _*（X）$与Hirzebruch同源性类别$ T_ {1*}（X）$之间的奇异品种平等。在本说明中，我们为基于立方高分辨率，分解定理和霍奇理论的投射品种提供了这种猜想的证明。证明的关键步骤是从立方高分辨率方面对理性同源性歧管进行了新的特征，我们发现了独立的兴趣。
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.
