Specialization of motivic Hodge-Chern classes

Abstract

In this paper we give a proof of the fact, that the motivic Hodge-Chern class transformation MHC_y and Hirzebruch class transformation MHT_y* for mixed Hodge modules and strictly specializable filtered D-modules commute with specialization in the algebraic and in a suitable complex analytic context. Here specialization in the Hodge- and D-module context means the corresponding nearby cycles defined in terms of the $V$-filtration of Malgrange-Kashiwara. This generalizes a corresponding specialization result of Verdier about MacPherson's Chern class transformation c_*.

comments are welcome

References in corpus (2)

• Hirzebruch classes and motivic Chern classes for singular spaces
• On the formalisme of mixed sheaves

Cited by in corpus (5)

• Characteristic classes of mixed Hodge modules
• Gysin Restriction of Topological and Hodge-Theoretic Characteristic Classes for Singular Spaces
• Characteristic classes of complex hypersurfaces
• Thom polynomials in $\mathcal{A}$-classification I: counting singular projections of a surface
• Hirzebruch-Milnor classes of complete intersections