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    Classification of Ding's Schubert Varieties: Finer Rook Equivalence

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    Dings Schubert.pdf (3.681Mb)
    Issue Date
    2007-02
    Author
    Develin, Mike
    Martin, Jeremy L.
    Reiner, Victor
    Publisher
    Canadian Mathematical Society
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Published Version
    https://cms.math.ca/10.4153/CJM-2007-002-9
    Version
    http://www.math.ca/cjm/v59/p36?abfmt=html
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    Abstract
    K.~Ding studied a class of Schubert varieties in type A partial flag manifolds, indexed by integer partitions \lambda and in bijection with dominant permutations. He observed that the Schubert cell structure of X_\lambda is indexed by maximal rook placements on the Ferrers board B_\lambda, and that the integral cohomology groups H^*(X_\lambda;\:\Zz), H^*(X_\mu;\:\Zz) are additively isomorphic exactly when the Ferrers boards B_\lambda, B_\mu satisfy the combinatorial condition of \emph{rook-equivalence}. We classify the varieties X_\lambda up to isomorphism, distinguishing them by their graded cohomology rings with integer coefficients. The crux of our approach is studying the nilpotence orders of linear forms in the cohomology ring.
    Description
    First published in The Canadian Journal of Mathematics, volume 59, no. 1, 2007, published by the Canadian Mathematical Society.
    URI
    http://hdl.handle.net/1808/6480
    DOI
    https://doi.org/10.4153/CJM-2007-002-9
    Collections
    • Mathematics Scholarly Works [282]
    Citation
    Classification of Ding's Schubert varieties: finer rook equivalence (with Mike Develin and Victor Reiner), Canadian Journal of Mathematics 59, no. 1 (2007), 36--62.

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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