Let S be a Desarguesian (t-1)-spread of PG(rt-1,q), $\Pi$. It is known that the Plucker embedding of the elements of S is a variety of PG(r^t-1,q), say V_{rt}. In this paper, we describe the image under the Plucker embedding of the elements of a linear set of PG(rt-1,q) of rank m 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 V_{rt}.
On some subvarieties of the Grassmann variety / Giuzzi, L; Pepe, Valentina. - In: LINEAR & MULTILINEAR ALGEBRA. - ISSN 0308-1087. - 63:11(2015), pp. 2121-2134. [10.1080/03081087.2014.983449]
On some subvarieties of the Grassmann variety
PEPE, VALENTINA
2015
Abstract
Let S be a Desarguesian (t-1)-spread of PG(rt-1,q), $\Pi$. It is known that the Plucker embedding of the elements of S is a variety of PG(r^t-1,q), say V_{rt}. In this paper, we describe the image under the Plucker embedding of the elements of a linear set of PG(rt-1,q) of rank m 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 V_{rt}.| File | Dimensione | Formato | |
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