Degree formula for Grassmann bundles

作者：Kaji Hajime^*; Terasoma Tomohide

来源：Journal of Pure and Applied Algebra, 2015, 219(12): 5426-5428.

DOI：10.1016/j.jpaa.2015.05.024

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

• 出版日期2015-12