### 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 language | English |
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Pages (from-to) | 5426-5428 |

Number of pages | 3 |

Journal | Journal of Pure and Applied Algebra |

Volume | 219 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2015 Dec 1 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Kaji, H., & Terasoma, T. (2015). Degree formula for Grassmann bundles.

*Journal of Pure and Applied Algebra*,*219*(12), 5426-5428. https://doi.org/10.1016/j.jpaa.2015.05.024