Corrigendum to the paper "Ovoidal packings of PG(3, q) for even q"
نویسندگان
چکیده
We show that any set of n pairwise disjoint ovals in a finite projective plane of even order has a unique common tangent. As a consequence, any set of q+1 pairwise disjoint ovoids in PG(3, q), q even, has exactly q2+1 common tangent lines, constituting a regular spread. Also, if q−1 ovoids in PG(3, q) intersect pairwise exactly in two given points x ̸= y and share two tangent planes πx, πy at these two points, then these ovoids share exactly (q + 1)2 common tangent lines, and they consist of the transversals to the pair xy, πx ∩ πy of skew lines. There is a similar (but more complicated) result for the common tangent lines to q ovoids in PG(3, q) which are mutually tangent at a common point and share a common tangent plane through this point. It is also shown that the common tangent lines to any pair of disjoint ovoids of PG(3, q), q even, form a regular spread.
منابع مشابه
Ovoidal blocking sets and maximal partial ovoids of Hermitian varieties
In [1], minimal large blocking sets in PG(3, q) and PG(4, q) havebeen constructed starting from ovoids of PG(3, q), Q(4, q) and Q(6, q).Some of these can be embedded in a hermitian variety as maximalpartial ovoids. In this paper, the geometric conditions assuring theseembeddings are established.References[1] F. Mazzocca, L. Storme and O. Polverino: Blocking sets in<l...
متن کاملGroup theoretic characterizations of Buekenhout – Metz unitals in PG ( 2 , q 2 )
Let G be the group of projectivities stabilizing a unital U in PG(2, q2) and let A,B be two distinct points of U . In this paper we prove that, if G has an elation group of order q with center A and a group of projectivities stabilizing both A and B of order a divisor of q − 1 greater than 2(√q − 1), then U is an ovoidal Buekenhout–Metz unital. From this result two group theoretic characterizat...
متن کاملNew Large (n, r)-arcs in PG(2, q)
An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in $PG(2, q)$ is denoted by $m_r(2,q)$. In this paper we present a new $(184,12)$-arc in PG$(2,17),$ a new $(244,14)$-arc and a new $(267,15$)-arc in $PG(2,19).$
متن کاملUniform Hyperplanes of Finite Dual Polar Spaces of Rank 3
Let 2 be a finite thick dual polar space of rank 3. We say that a hyperplane H of 2 is locally singular (respectively, quadrangular or ovoidal) if H & Q is the perp of a point (resp. a subquadrangle or an ovoid) of Q for every quad Q of 2. If H is locally singular, quadrangular, or ovoidal, then we say that H is uniform. It is known that if H is locally singular, then either H is the set of poi...
متن کاملMultipliers of pg-Bessel sequences in Banach spaces
In this paper, we introduce $(p,q)g-$Bessel multipliers in Banach spaces and we show that under some conditions a $(p,q)g-$Bessel multiplier is invertible. Also, we show the continuous dependency of $(p,q)g-$Bessel multipliers on their parameters.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 341 شماره
صفحات -
تاریخ انتشار 2018