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．Seminars

	NCTS Seminar in Algebraic Geometry

14:00 - 15:00, October 24, 2019 (Thursday)
R440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
Degree Formula for Grassmann Bundles
Hajime Kaji (Waseda University)

Abstract:

The Grassmann bundle $\mathbb G_{X}(d, \mathcal E)$ of $d$ -planes associated to a vector bundle $\mathcal E$ on a scheme $X$ is by definition a fibre bundle whose fibre at each point $x \in X$ is isomorphic to the Grassmann variety $\mathbb G(d, \mathcal E\otimes k(x))$ of $d$ -planes in the vector space $\mathcal E\otimes k(x)$ . If $X$ is projective over a field and $\mathcal E$ is very ample, then $\mathbb G_{X}(d, \mathcal E)$ is naturally embedded into a projective space with relative Plücker embedding over $X$ . In this talk I explain a degree formula for $\mathbb G_{X}(d, \mathcal E)$ . This is a jointwork with T. Terasoma.