Non-projective embeddings in the Grassmann variety

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• 作者：Ilaria Cardinali ^{ilaria.cardinali@unisi.it}
• 关键词：Dual classical thick generalized quadrangles ; Grassmann embedding ; veronese embedding
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2013
• 出版时间：15 May, 2013
• 年：2013
• 卷：40
• 期：Complete
• 页码：53-57
• 全文大小：159 K

文摘

We investigate properties of the grassmann embedding of dual classical thick generalized quadrangles focusing on the Grassmann embedding of the dual of an orthogonal quadrangle and the dual of a hermitian quadrangle . We prove that, if the characteristic of the field is different from 2 then the dimension of the grassmann embedding of is 10 and its image is isomorphic to the quadratic veronese variety of a 3-dimensional projective space. If is a perfect field of characteristic 2 then the dimension of the grassmann embedding of is proved to be 9 and its image is a 3-dimensional algebraic subvariety of the Grassmannian of lines of a 4-dimensional projective space. Moving to consider the dual quadrangle , we prove that the dimension of its Grassmann embedding is 10 and the image of under the Grassmann embedding is a 2-dimensional algebraic subvariety of the Grassmannian of lines of a 4-dimensional projective space.