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October, 1999 Configurations of seven lines on the real projective plane and the root system of type E7
J. Math. Soc. Japan 51(4): 987-1013 (October, 1999). DOI: 10.2969/jmsj/05140987


Let l1,l2,...,l7 be mutually different seven lines on the real projective plane. We consider two conditions;(A) No three of l1,l2,...,l7 intersect at a point. (B) There is no conic tangent to any six of l1,l2, . . . , l7. Cummings [3] and White [16] showed that there are eleven non-equivalent classes of systems of seven lines with condition (A)(cf. [7], Chap. 18). The purposes of this article is to give an interpretation of the classification of Cummings and White in terms of the root system of type E7. To accomplish this, it is better to add condition (B) for systems of seven lines. Moreover we need the notion of tetrahedral sets which consist of ten roots modulo slgns in the root system of type E7 and which plays an important role in our study.


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Jiro SEKIGUCHI. "Configurations of seven lines on the real projective plane and the root system of type E7." J. Math. Soc. Japan 51 (4) 987 - 1013, October, 1999.


Published: October, 1999
First available in Project Euclid: 10 June 2008

zbMATH: 0948.52010
MathSciNet: MR1705257
Digital Object Identifier: 10.2969/jmsj/05140987

Primary: 52B30
Secondary: 51F15 , 51M30

Keywords: Arrangements of lines , configuration spaces , Root systems , Tetradiagrams , the real projective plane

Rights: Copyright © 1999 Mathematical Society of Japan

Vol.51 • No. 4 • October, 1999
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