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Grassmannian of $k((z))$: Picard Group, Equations and Automorphisms

Francisco J. Plaza Martín
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Abstract

This paper aims at generalizing some geometric properties of Grassmannians of finite dimensional vector spaces to the case of Grassmannnians of infinite dimensional ones, in particular for that of $k((z))$. It is shown that the Determinant Line Bundle generates its Picard Group and that the Plücker equations define it as closed subscheme of a infinite projective space. Finally, a characterization of finite dimensional projective spaces in Grassmannians allows us to offer an approach to the study of the automorphism group.

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BibTeXRIS

Francisco J. Plaza Martín. 1998-01-30. Grassmannian of $k((z))$: Picard Group, Equations and Automorphisms. https://arxiv.org/abs/math/9801138

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