Degree formula for Grassmann bundles

Hajime Kaji, Tomohide Terasoma

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    Abstract

    Let X be a non-singular quasi-projective variety over a field, and let E be a vector bundle over X. Let GX(d,E) be the Grassmann bundle of E over X parametrizing corank d subbundles of E with projection π:GX(d,E)→X, let Q←π*E be the universal quotient bundle of rank d, and denote by θ the Plücker class of GX(d,E), that is, the first Chern class of the Plücker line bundle, det<>Q. In this short note, a closed formula for the push-forward of powers of the Plücker class θ is given in terms of the Schur polynomials in Segre classes of E, which yields a degree formula for GX(d,E) with respect to θ when X is projective and dE is very ample.

    Original languageEnglish
    Pages (from-to)5426-5428
    Number of pages3
    JournalJournal of Pure and Applied Algebra
    Volume219
    Issue number12
    DOIs
    Publication statusPublished - 2015 Dec 1

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    ASJC Scopus subject areas

    • Algebra and Number Theory

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