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  • 1
    Electronic Resource
    Electronic Resource
    Partial Flocks of Quadratic Cones with a Point Vertex in Pg(n,q), n Odd (1997)
    Springer
    Journal of algebraic combinatorics 6 (1997), S. 377-392 
    Details
    ISSN: 1572-9192
    Keywords: Galois geometry ; flock ; cone ; ovoid ; cap
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalise the definition and many properties of flocks ofquadratic cones in PG(3,q) to partial flocks of quadratic coneswith vertex a point in PG(p,q), for n ≥ 3 odd.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008677211380
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  • 2
    Electronic Resource
    Electronic Resource
    Ovoids with a pencil of translation ovals (1996)
    Springer
    Geometriae dedicata 62 (1996), S. 19-34 
    Details
    ISSN: 1572-9168
    Keywords: 51E20 ; Ovoids ; translation ovals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that if an ovoid of PG(3, q), where q〉2 is even, has a pencil of translation ovals and if the carrier of the pencil is not an axis of at least one of the ovals in the pencil, then the ovoid is a Tits ovoid. It follows, as a corollary of this and a result of Penttila and Praeger, that if an ovoid of PG(3, q), where q〉2 is even, has a pencil of translation ovals then the ovoid is either an elliptic quadric or a Tits ovoid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00239999
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  • 3
    Electronic Resource
    Electronic Resource
    Characterizations of Buekenhout-Metz unitals (1996)
    Springer
    Geometriae dedicata 59 (1996), S. 29-42 
    Details
    ISSN: 1572-9168
    Keywords: 51E20 ; Buekenhout-Metz unitals ; classical unitals ; Baer sublines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a characterization of the Buekenhout-Metz unitals in PG(2, q 2), in the cases that q is even or q=3, in terms of the secant lines through a single point of the unital. With the addition of extra conditions, we obtain further characterizations of Buekenhout-Metz unitals in PG(2, q 2), for all q. As an application, we show that the dual of a Buekenhout-Metz unital in PG(2, q 2) is a Buekenhout-Metz unital.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181524
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  • 4
    Electronic Resource
    Electronic Resource
    Ovoids and monomial ovals (1996)
    Springer
    Geometriae dedicata 59 (1996), S. 223-241 
    Details
    ISSN: 1572-9168
    Keywords: 51E21 ; ovoids ; monomial ovals ; Tits ovoid ; finite geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is a contribution to the classification of ovoids. We show, under some rather technical assumptions, that if an ovoid of PG(3, q) has a pencil of monomial ovals, then it is either an elliptic quadric or a Tits ovoid. Further, we show that if an ovoid of PG(3, q) has a bundle of translation ovals, again under some extra assumptions, then the ovoid is an elliptic quadric or a Tits ovoid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181693
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  • 5
    Electronic Resource
    Electronic Resource
    Characterisations of Flock Quadrangles (2000)
    Springer
    Geometriae dedicata 82 (2000), S. 171-191 
    Details
    ISSN: 1572-9168
    Keywords: generalized quadrangles ; flocks ; ovals ; translation planes.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We characterise the Hermitian and Kantor flock generalized quadrangles of order (q 2,q), q even, (associated with the linear and Fisher–Thas–Walker flocks of a quadratic cone, and the Desarguesian and Betten–Walker translation planes) in terms of a self-dual subquadrangle. Equivalently, we show that a herd which contains a translation oval must be associated with the linear or Fisher–Thas–Walker flock. This result is a consequence of the determination of all functions which satisfy a certain absolute trace equation whose form is remarkably similar to that of an equation arising in recent studies of ovoids in three-dimensional projective space of finite order q.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005153406421
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  • 6
    Electronic Resource
    Electronic Resource
    Projective spread sets (1990)
    Springer
    Journal of geometry 37 (1990), S. 55-76 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper the notion of a spread set for at-spread ofPG(2t+1,q) is generalised and it is shown that certaint-spreads ofPG(n, q) correspond to these generalised spread sets. Then a projective spread set is defined and it is shown that anyt-spread ofPG(n, q) corresponds to a projective spread set. Connections between the spread set and the projective spread set of at-spread are discussed, in particular in the case of at-spread ofPG(2t + 1,q) the spread set and the projective spread set are equivalent, giving a new and straightforward construction of a spread set. The methods developed are used to show, with the aid of a computer, that the 1-packing ofPG(7,2) constructed by Baker is regulus-free.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01230359
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  • 7
    Electronic Resource
    Electronic Resource
    Ovoids ofPG(3, 16) are elliptic quadrics, II (1992)
    Springer
    Journal of geometry 44 (1992), S. 140-159 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous paper [8] the authors have shown that every ovoid ofPG(3, 16) is an elliptic quadric. The arguments used a computer and also depended on the computer-aided classification of hyperovals ofPG(2, 16) (see [3]). Recently (see [9]) the classification of hyperovals ofPG(2,16) has been obtained without the use of a computer. The present paper completes a computer-free proof that every ovoid ofPG(3,16) is an elliptic quadric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228289
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  • 8
    Electronic Resource
    Electronic Resource
    Classification of ovoids inPG(3, 32) (1994)
    Springer
    Journal of geometry 50 (1994), S. 143-150 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A classification of the ovoids inPG(3, 32) is completed with the aid of a computer. The ovoids are examined in terms of which ovals can possibly appear as secant plane sections. A weak necessary condition for two ovals to appear together as plane sections of an ovoid surprisingly turns out to be sufficient to demonstrate that the only possible secant plane sections are translation ovals. A known result regarding ovoids with such plane sections then identifies the ovoids as either elliptic quadrics or Tits ovoids.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01222671
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  • 9
    Electronic Resource
    Electronic Resource
    Arcs fixed byA 5 andA 6 (1996)
    Springer
    Journal of geometry 55 (1996), S. 123-138 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The complete list of thek-arcsK inPG(n, q) fixed by a projective group isomorphic toA 5 orA 6, which acts primitively on the points ofK, is presented. This leads to new classes of 10-arcs inPG(n, q), 3 ≤n ≤5. Our results also show that the non-classical 10-arc inPG(4, 9), discovered by D.G. Glynn [3], belongs to an infinite class of 10-arcs inPG(4, 3h),h ≥2, fixed by a projective group isomorphic toA 6.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223038
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  • 10
    Electronic Resource
    Electronic Resource
    A new hyperoval inPG(2, 32) (1992)
    Springer
    Journal of geometry 44 (1992), S. 117-139 
    Details
    ISSN: 1420-8997
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new hyperoval is constructed in the Desarguesian projective planePG(2, 32). It has a full collineation stabiliser of order 3. It is also shown, with the aid of a computer, that the collineation stabiliser of any further new hyperoval is either trivial or has order 2 with the generator fixing no point on the hyperoval.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01228288
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