2015/04/14 by Hajime Kaji, Kaji, H., Tomohide Terasoma +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1504.03400
openalex publication_date 2015/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a non-singular quasi-projective variety over a field, and let \mathcal E be a vector bundle over X. Let \mathbb GX(d, \mathcal E) be the Grassmann bundle of \mathcal E over X parametrizing corank d subbundles of \mathcal E, and denote by θ the Plücker class of \mathbb GX(d, \mathcal E), that is, the first Chern class of the universal quotient bundle over \mathbb GX(d, \mathcal E). In this short note, a closed formula for the push-forward of powers of θ is given in terms of the Schur polynomials in Segre classes of \mathcal E, which yields a degree formula for \mathbb GX(d, \mathcal E) with respect to θ when X is projective and \wedge d \mathcal E is very ample.