# Degree formula for Grassmann bundles

Hajime Kaji*, Tomohide Terasoma

*この研究の対応する著者

1 被引用数 (Scopus)

## 抄録

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.

本文言語 English 5426-5428 3 Journal of Pure and Applied Algebra 219 12 https://doi.org/10.1016/j.jpaa.2015.05.024 Published - 2015 12月 1

• 代数と数論

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