Homology, Homotopy and Applications

Volume 18 (2016)

Number 2

Motivic and derived motivic Hirzebruch classes

Pages: 283 – 301

DOI: http://dx.doi.org/10.4310/HHA.2016.v18.n2.a16

Authors

Jean-Paul Brasselet (Institute de Mathématiques, Aix-Marseille Université, Marseille, France)

Jörg Schürmann (Mathematische Institut, Westfälische Wilhelms-Universität, Münster, Germany)

Shoji Yokura (Department of Mathematics and Computer Science, Graduate School of Science and Engineering, Kagoshima University, Korimoto, Kagoshima, Japan)

Abstract

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.

Keywords

higher Euler characteristic, arithmetic genus, signature, Hirzebruch genus, homology, Chern class, Todd class, $L$-class, motivic Hirzebruch class

2010 Mathematics Subject Classification

14C17, 14C40, 14F25, 14F45, 14Q15, 32S35

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