Brasselet, Jean-Paul; Schürmann, Jörg; Yokura, Shoji Motivic and derived motivic Hirzebruch classes. (English) Zbl 1354.14012 Homology Homotopy Appl. 18, No. 2, 283-301 (2016). Summary: In this paper we give a formula for the Hirzebruch \(\chi_y\)-genus \(\chi_y(X)\) and similarly for the motivic Hirzebruch class \(T_{y\ast}(X)\) 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. Cited in 3 Documents MSC: 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14C40 Riemann-Roch theorems 14F25 Classical real and complex (co)homology in algebraic geometry 14F45 Topological properties in algebraic geometry 14Q15 Computational aspects of higher-dimensional varieties 32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects) Keywords:higher Euler characteristic; arithmetic genus; signature; Hirzebruch genus; homology; Chern class; Todd class; \(L\)-class; motivic Hirzebruch class PDFBibTeX XMLCite \textit{J.-P. Brasselet} et al., Homology Homotopy Appl. 18, No. 2, 283--301 (2016; Zbl 1354.14012) Full Text: DOI arXiv