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Segre classes and Damon–Kempf–Laksov formula in algebraic cobordism

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In this paper we extend to algebraic cobordism the classical Damon–Kempf–Laksov formula, which expresses the Chow ring Schubert classes of Grassmann bundles as Schur determinants in Chern classes. The basic building block of our closed formula, which is written as a sum of determinants, is represented by a generalisation of Segre classes that we introduce and describe.

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Acknowledgements

Both authors would like to thank Takeshi Ikeda for useful discussions and Marc Levine for his valuable comments which greatly improved the readability. Thanks are also due to the anonymous referee, whose observations and suggestions significantly enhanced the presentation. This research was conducted while the first author was affiliated to KAIST, where he was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (ASARC, NRF-2007-0056093). This work was then brought to completion in the framework of the research training group GRK 2240: Algebro-Geometric Methods in Algebra, Arithmetic and Topology, which is funded by the DFG. The second author is supported by Grant-in-Aid for Young Scientists (B) 16K17584.

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Authors and Affiliations

  1. Fachgruppe Mathematik und Informatik, Bergische Universität Wuppertal, Gaußstrasse 20, 42119, Wuppertal, Germany

    Thomas Hudson

  2. Department of Applied Mathematics, Okayama University of Science, Okayama, 700-0005, Japan

    Tomoo Matsumura

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  1. Thomas Hudson
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  2. Tomoo Matsumura
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Correspondence to Thomas Hudson.

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Communicated by Vasudevan Srinivas.

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Hudson, T., Matsumura, T. Segre classes and Damon–Kempf–Laksov formula in algebraic cobordism. Math. Ann. 374, 1439–1457 (2019). https://doi.org/10.1007/s00208-019-01839-y

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