Grassmann embeddings of polar Grassmannians
Abstract
In this paper we compute the dimension of the Grassmann embeddings of the polar Grassmannians associated to a possibly degenerate Hermitian, alternating or quadratic form with possibly nonmaximal Witt index. Moreover, in the characteristic $2$ case, when the form is quadratic and nondegenerate with bilinearization of minimal Witt index, we define a generalization of the socalled Weyl embedding (see [I. Cardinali and A. Pasini, Grassmann and Weyl embeddings of orthogonal Grassmannians. J. Algebr. Combin. 38 (2013), 863888]) and prove that the Grassmann embedding is a quotient of this generalized "Weyllike" embedding. We also estimate the dimension of the latter.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1810.12811
 Bibcode:
 2018arXiv181012811C
 Keywords:

 Mathematics  Algebraic Geometry;
 51A50;
 14M15;
 15A75
 EPrint:
 25 pages/revised version after review