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Motivic Chern Classes of Cones

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Singularities and Their Interaction with Geometry and Low Dimensional Topology

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Abstract

We study motivic Chern classes of cones. First we show examples of projective cones of smooth curves such that their various K-classes (sheaf theoretic, push-forward and motivic) are all different. Then we show connections between the torus equivariant motivic Chern class of a projective variety and of its affine cone, generalizing results on projective Thom polynomials.

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Acknowledgements

I am grateful for Andrzej Weber for patiently explaining me the intricacies of the motivic Chern class. I had inspiring conversations on the topic with Richárd Rimányi, András Némethi, Ákos Matszangosz and Balázs Kőműves. A special case of Theorem 4.4 was first proved by the latter. I thank Anders Buch for explaining the role of the Cohen-Macaulay condition in pulling back the sheaf theory K-class.

The author László M. Fehér was partially supported by NKFI 112703 and 112735 and NKFIH KKP 126683 as well as ERC Advanced Grant LTDBud and enjoyed the hospitality of the Rènyi Institute.

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Authors and Affiliations

  1. Institute of Mathematics, Eötvös University, Budapest, Hungary

    László M. Fehér

Authors
  1. László M. Fehér
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Editors and Affiliations

  1. Basque Center for Applied Mathematics Ikerbasque (Basque Foundation for Science), Bilbao, Spain

    Javier Fernández de Bobadilla

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania

    Tamás László

  3. Alfréd Rényi Institute of Mathematics, Budapest, Hungary

    András Stipsicz

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Fehér, L.M. (2021). Motivic Chern Classes of Cones. In: Fernández de Bobadilla, J., László, T., Stipsicz, A. (eds) Singularities and Their Interaction with Geometry and Low Dimensional Topology . Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-61958-9_9

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