The uniqueness theorem for Gysin coherent characteristic classes of singular spaces - Banagl, Markus; Wrazidlo, Dominik (Journal of the London Mathematical Society, 2023)
We establish a general computational scheme designed for a systematic computation of characteristic classes of singular complex algebraic varieties that satisfy a Gysin axiom in a transverse setup. This scheme is explicitly geometric and of a recursive nature terminating on genera of explicit characteristic subvarieties that we construct. It enables us, for example, to apply intersection theory of Schubert varieties to obtain a uniqueness result for such characteristic classes in the homology of an ambient Grassmannian. Our framework applies in particular to the Goresky-MacPherson LŁ\-class by virtue of the Gysin restriction formula obtained by the first author in previous work. We illustrate our approach for a systematic computation of the LŁ\-class in terms of normally nonsingular expansions in examples of singular Schubert varieties that do not satisfy Poincaré duality over the rationals.
Online veröffentlicht: 13. Oktober 2023
Gesehen am 15.12.2023