Motivic and derived motivic Hirzebruch classes

摘要

In this paper we give a formula for the Hirzebruch $chi_y$-genus $chi_y(X)$ and similarly for the motivic Hirzebruch class $T_{y*}(X)$ for possibly singular varieties $X$, using the Vandermonde matrix. Motivated by the notion of secondary Euler characteristic and higher Euler characteristic, we consider a similar notion for the motivic Hirzebruch class, which we call a derived motivic Hirzebruch class.