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Motivic and derived motivic Hirzebruch classes. (English) Zbl 1354.14012

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.

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)
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