The quintic Grassmannian \(\mathcal G_{1, 4, 2}\) in PG(9, 2)
In this paper is studied the case \({\mathcal G}_{1,4,2}\subset \text{PG}(9,2)\) of the Grassmannian \({\mathcal G}_{1,4,2}\) of the lines of \(\text{PG}(4,2)\), for which a determined quintic \(Q\) has reduced degree \(5\). This structure is given explicitly by the authors in J. Comb. Theory, Ser. A 68, No.~1, 226--231 (1994; Zbl 0809.05022). The aim of this article is to study the associate \(X^\#\) of flats \(X\subset\text{PG}(9,2)\), as defined in terms of the completely polarized form \(Q^{++}\) of the quintic \(Q\). The associate \(X^\#\) is a generalization to \(\deg Q> 2\) of the orthogonal complement \(X^\perp\) in the case \(\deg Q= 2\).
scientific article; zbMATH DE number 2091529