Nearby cycles and characteristic classes of singular spaces
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Publication:5501439
DOI10.4171/118-1/11zbMATH Open1317.14015arXiv1003.2343OpenAlexW4231659018MaRDI QIDQ5501439
Author name not available (Why is that?)
Publication date: 3 August 2015
Published in: (Search for Journal in Brave)
Abstract: In this paper we give an introduction to our recent work on characteristic classes of complex hypersurfaces based on some talks given at conferences in Strasbourg, Oberwolfach and Kagoshima. We explain the relation between nearby cycles for constructible functions or sheaves as well as for (relative) Grothendieck groups of algebraic varieties and mixed Hodge modules, and the specialization of characteristic classes of singular spaces like the Chern-, Todd-, Hirzebruch- and motivic Chern-classes. As an application we get a description of the differences between the corresponding virtual and functorial characteristic classes of complex hypersurfaces in terms of vanishing cycles related to the singularities of the hypersurface.
Full work available at URL: https://arxiv.org/abs/1003.2343
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