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Some noteworthy alternating trilinear forms

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Abstract

Given an alternating trilinear form \({T\in\text{Alt}(\times^{3}V_{n})}\) on \({V_{n}=V(n,\mathbb{F})}\) let \({\mathcal{L}_{T}}\) denote the set of T-singular lines in \({\text{PG}(n-1)=\mathbb{P}V_{n},}\) consisting that is of those lines \({\langle a,b\rangle}\) of \({\text{PG}(n-1)}\) such that T(a, b, x) = 0 for all \({x\in V_{n}.}\) Amongst the immense profusion of different kinds of T we single out a few which we deem noteworthy by virtue of the special nature of their set \({\mathcal{L}_{T}}\).

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, TheNetherlands

    Jan Draisma

  2. Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

    Jan Draisma

  3. Centre for Mathematics, University of Hull, Hull, HU6 7RX, UK

    Ron Shaw

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  1. Jan Draisma
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  2. Ron Shaw
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Correspondence to Jan Draisma.

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Draisma, J., Shaw, R. Some noteworthy alternating trilinear forms. J. Geom. 105, 167–176 (2014). https://doi.org/10.1007/s00022-013-0202-2

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  • DOI: https://doi.org/10.1007/s00022-013-0202-2

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