Let  be a Desarguesian (t−1)--spread of PG(rt−1,q), Π a m-dimensional subspace of PG(rt−1,q) and Λ the linear set consisting of the elements of  with non-empty intersection with Π. It is known that the Pl\"{u}cker embedding of the elements of  is a variety of PG(rt−1,q), say rt. In this paper, we describe the image under the Pl\"{u}cker embedding of the elements of Λ and we show that it is an m-dimensional algebraic variety, projection of a Veronese variety of dimension m and degree t, and it is a suitable linear section of rt.

On some subvarieties of the Grassmann variety

GIUZZI, Luca;
2015-01-01

Abstract

Let  be a Desarguesian (t−1)--spread of PG(rt−1,q), Π a m-dimensional subspace of PG(rt−1,q) and Λ the linear set consisting of the elements of  with non-empty intersection with Π. It is known that the Pl\"{u}cker embedding of the elements of  is a variety of PG(rt−1,q), say rt. In this paper, we describe the image under the Pl\"{u}cker embedding of the elements of Λ and we show that it is an m-dimensional algebraic variety, projection of a Veronese variety of dimension m and degree t, and it is a suitable linear section of rt.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/422306
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