The uniqueness theorem for Gysin coherent characteristic classes of singular spaces

• Verfasst von: Banagl, Markus [VerfasserIn]
• Verfasst von: Wrazidlo, Dominik [VerfasserIn]
• Titel: The uniqueness theorem for Gysin coherent characteristic classes of singular spaces
• Verf.angabe: Markus Banagl, Dominik J. Wrazidlo
• E-Jahr: 2023
• Jahr: 13 October 2023
• Umfang: 45 S.
• Illustrationen: Illustrationen
• Fussnoten: Online veröffentlicht: 13. Oktober 2023 ; Gesehen am 15.12.2023
• Titel Quelle: Enthalten in: London Mathematical SocietyJournal of the London Mathematical Society
• Ort Quelle: Oxford : Wiley, 1926
• Jahr Quelle: 2023
• Band/Heft Quelle: (2023), online ahead of print
• ISSN Quelle: 1469-7750
• DOI: doi:10.1112/jlms.12823
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1876202068

Abstract

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 L\L\-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 L\L\-class in terms of normally nonsingular expansions in examples of singular Schubert varieties that do not satisfy Poincaré duality over the rationals.