Spreads and Ovoids Translation with Respect to Disjoint Flags

ALAN OFFER; HENDRIK VAN MALDEGHEM

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Spreads and Ovoids Translation with Respect to Disjoint Flags

机译：关于不相交标志的传播和避免翻译

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摘要

It is shown that if a spread of a finite split Cayley hexagon is translation with respect to two disjoint flags then it is either a hermitian spread or a Ree-Tits spread. Analogously, if an ovoid of a classical generalized quadrangle Q(4, q) is translation with respect to two disjoint flags then it is either an elliptic quadric or a Suzuki-Tits ovoid. In the course of obtaining these results, we introduce the notion of local polarity for ovoid-spread pairings and show that if an ovoid-spread pairing is locally polar at each of its elements then it arises from a polarity.

机译：结果表明，如果有限分裂的Cayley六边形的展宽相对于两个不相交的标志平移，那么它要么是Hermitian展宽，要么是Ree-Tits展宽。类似地，如果相对于两个不相交的标志平移经典广义四边形Q（4，q）的卵形，则它要么是椭圆形二次形，要么是Suzuki-Tits卵形。在获得这些结果的过程中，我们引入了卵形扩展配对的局部极性的概念，并表明，如果卵形扩展配对在其每个元素上都是局部极性的，则它是由极性引起的。

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来源
《Designs, Codes and Crytography》 |2004年第3期|p.351-367|共17页
作者
ALAN OFFER; HENDRIK VAN MALDEGHEM;
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作者单位

Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Gent, Belgium;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类高等数学;
关键词
translation spread; translation ovoid; generalized polygon; split cayley hexagon; polarity;

机译：平移传播;平移卵形;广义多边形;开曼六边形;极性;

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专利

1. Generalized quadrangles with an ovoid that is translation with respect to opposite flags [J] . Offer A, Thas K, Van Maldeghem H Archiv der Mathematik . 2005,第4期

机译：具有相对于相对标志平移的卵形的广义四边形
2. Generalized quadrangles with an ovoid that is translation with respect to opposite flags [J] . Alan Offer, Koen Thas, Hendrik Van Maldeghem Archiv der Mathematik . 2005,第4期

机译：具有相对于相对标志平移的卵形的广义四边形
3. Translation Ovoids and Spreads of the Generalized Hexagon H(q) [J] . Alan Offer Geometriae Dedicata . 2001,第1a3期

机译：广义六边形H（q）的平移卵形和扩散
4. Ovoids, spreads and m-systems of finite classical polar spaces [C] . J. A. Thas British Combinatorial Conference . 2001

机译：有限古典极地空间的卵形，涂抹和M系统
5. Constrained inversion of gravity data over the Ovoid and Mini-Ovoid in the Voisey's Bay nickel-copper-cobalt deposit, Labrador. [D] . Ash, Michael R. 2007

机译：拉布拉多Voisey湾镍铜钴矿床中卵形和微型卵形的重力数据反演受限。
6. Wastewater as a red flag in COVID-19 spread [O] . Pierfrancesco Lapolla, Regent Lee, Andrea Mingoli -1

机译：废水作为Covid-19蔓延的红旗
7. New bounds for partial spreads of H(2d−1,q2) and partial ovoids of the Ree–Tits octagon [O] . Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 9190401, Israel ( host institution ), Ihringer, Ferdinand ( author ), Sin, Peter ( UF author ), 2018

机译：H（2d-1，q2）的部分扩散和Ree-Tits八边形的部分卵形的新界

Spreads and Ovoids Translation with Respect to Disjoint Flags

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