Flocks of Infinite Hyperbolic Quadrics
نویسنده
چکیده
Let K be a field containing a nonsquare γ and F = K (√γ ) a quadratic extension. Let σ denote the unique involutory automorphism of F fixing K pointwise. For every field K such that the nonzero squares of K do not form an index 1 or 2 subgroup of (K ( √ γ )∗)σ+1 = K−, a construction is given which produces large numbers of infinite nearfield and non nearfield flocks of an infinite hyperbolic quadric in PG(3, K ).
منابع مشابه
Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems
We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of type D4, F4, H4, respectively. The smallest member of each of these families is an exceptional flock. We then characterise these partial flocks in terms of the rectangle condition of Benz and by not be...
متن کاملPartial Flocks of Non-Singular Quadrics in <Emphasis Type="Italic">PG</Emphasis>(2<Emphasis Type="Italic">r</Emphasis> + 1, <Emphasis Type="Italic">q</Emphasis>)
We generalise the definition and many properties of partial flocks of non-singular quadrics in PG(3, q) to partial flocks of non-singular quadrics in PG(2r + 1, q).
متن کاملOptical properties of a semi-infinite medium consist of graphene based hyperbolic meta-materials with tilted optical axis
In this paper, the optical properties of a semi-infinite medium composed of graphen-based hyperbolic meta-materials with the optical axis were tilted with respect to its boundary with air, by using the Maxwell equations; then the homogeneous effective medium approximation method was studied. The results showed that the orientation of the structure layers (geometric induced anisotropy) affec...
متن کاملHyperbolic Fibrations of PG(3, q)
A hyperbolic bration is set of q ?1 hyperbolic quadrics and two lines which together partition the points of PG(3; q). The classical example of a hyperbolic bration comes from a pencil of quadrics; however, several other families are known. In this paper we construct a new family of hyperbolic brations for odd prime powers q. As an application of hyperbolic brations, we note that they can be us...
متن کاملCharacterization results on small blocking sets
In [8], De Beule and Storme characterized the smallest blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 4; they proved that these blocking sets are truncated cones over the unique ovoid of Q+(7, 3). We continue this research by classifying all the minimal blocking sets of the hyperbolic quadrics Q+(2n + 1, 3), n ≥ 3, of size at most 3n + 3n−2. This means that the three smallest minim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996