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On parametrized rational curves in Grassmann varieties. (English) Zbl 0625.14027

Space curves, Proc. Conf., Rocca di Papa/Italy 1985, Lect. Notes Math. 1266, 251-272 (1987).
[For the entire collection see Zbl 0614.00006.]
The purpose of the paper is to give information on a certain smooth compactification of the space of all morphisms of a given degree from \({\mathbb{P}}^ 1\) to a Grassmann variety. This scheme is the Grothendieck Quot scheme of quotients of a trivial vector bundle on \({\mathbb{P}}^ 1\). We compute the additve and the multiplicative structure of its Chow ring and identify the ample cone and the corresponding projective embeddings.

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14H10 Families, moduli of curves (algebraic)
14C05 Parametrization (Chow and Hilbert schemes)
14M17 Homogeneous spaces and generalizations
14D20 Algebraic moduli problems, moduli of vector bundles

Citations:

Zbl 0614.00006