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Joerg Schuermann

  1. Motivic Bivariant Characteristic Classes.

    Ср, 10/12/2011 - 15:01 — SomNambul
    Authors: Joerg Schuermann, Shoji Yokura
    Subjects: Algebraic Geometry
    Abstract

    Let K_0(V/X) be the relative Grothendieck group of varieties over X in
    obj(V), with V the category of (quasi-projective) algebraic (resp. compact
    complex analytic) varieties over a base field k. Then we constructed the
    motivic Hirzebruch class transformation in the algebraic context for k of
    characteristic zero and in the compact complex analytic context. It unifies the
    well-known three characteristic class transformations of singular varieties:
    MacPherson's Chern class, Baum-Fulton-MacPherson's Todd class and the L-class
    of Goresky-MacPherson and Cappell-Shaneson.

  2. Hirzebruch classes of complex hypersurfaces.

    Втр, 08/25/2009 - 22:41 — SomNambul
    Authors: Sylvain E. Cappell, Laurentiu Maxim, Joerg Schuermann, Julius L. Shaneson
    Subjects: Algebraic Topology
    Abstract

    The Milnor-Hirzebruch class of a locally complete intersection X in an
    algebraic manifold M measures the difference between the (Poincare dual of the)
    Hirzebruch class of the virtual tangent bundle of X and, respectively, the
    Brasselet-Schuermann-Yokura (homology) Hirzebruch class of X. In this note, we
    calculate the Milnor-Hirzebruch class of a globally defined algebraic
    hypersurface X in terms of the corresponding Hirzebruch invariants of singular
    strata in a Whitney stratification of X.

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