The uniqueness theorem for Gysin coherent characteristic classes of singular spaces
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 charac...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
13 October 2023
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| In: |
Journal of the London Mathematical Society
Year: 2023, Pages: 1-45 |
| ISSN: | 1469-7750 |
| DOI: | 10.1112/jlms.12823 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1112/jlms.12823 Verlag, kostenfrei, Volltext: https://onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12823 
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| Author Notes: | Markus Banagl, Dominik J. Wrazidlo |
| Summary: | 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. |
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| Item Description: | Online veröffentlicht: 13. Oktober 2023 Gesehen am 15.12.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1469-7750 |
| DOI: | 10.1112/jlms.12823 |