Mar 26, 2015 · Book Description Originally published in 1911 as number thirteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book presents a general survey of the problem of the 27 lines upon the cubic surface. Illustrative figures and a bibliography are also included. Ludwig Schläfli An attempt to determine the twenty-seven lines upon a surface of the third order, and to divide such surfaces into species in reference to the reality of the lines upon the surface, Quarterly J. Math. 2 55–56; Gesammelte Mathematische Abhandlungen, 2 198–218 Birkhäuser, Basel, 1953. The twenty-seven lines upon the cubic surface. by Archibald Henderson. Henderson, Archibald 2015 [1911], The twenty-seven lines upon the cubic surface, Cambridge Tracts in Mathematics, Cambridge University Press, ISBN 978-1107493513, JFM 42.0661.01 Holzer, Stephan; Labs, Oliver 2006, "Illustrating the classification of real cubic surfaces" PDF, Algebraic geometry and geometric modeling, Springer, pp. 119.

[11] Archibald Henderson, The Twenty-Seven Lines upon the Cubic Surface, Cam-bridge University Press, 1911. [12] Marta Panizzut - Emre Can Sertoz - Bernd Sturmfels,¨ An Octanomial Model for Cubic Surfaces, arXiv preprint arXiv:1908.06106 2019. [13] Miles Reid, Undergraduate Algebraic Geometry, Cambridge University Press Cambridge, 1988. Oct 16, 2006 · Cite this chapter as: Hunt B. 1996 The 27 lines on a cubic surface. In: The Geometry of some special Arithmetic Quotients. Lecture Notes in Mathematics, vol 1637. Jul 02, 2013 · In the previous post, we introduced the Fano scheme of a subscheme of projective space, as the Hilbert scheme of planes of a certain dimension on that subscheme. In this post, I’d like to work out an explicit example, of the 27 lines on a smooth cubic surface in; as we’ll see, the Fano scheme is 27 reduced points, and the count can be made with a little calculation on the Grassmannian.

Feb 15, 2016 · This surface omits some points in the Clebsch cubic, which have become ‘points at infinity’. The picture above is a rotating view of this surface, the 27 lines on this surface, and 7 of the 10 Eckardt points: points where 3 lines meet. The remaining 3 Eckardt points are at infinity. [11] Archibald Henderson, The T wenty Seven Lines on the Cubic Surface, Cambridge Uni- versity Press, 1911. [12] Douglas MacHale, My favourite polynomial, M athematical Gazette 75 1991, 157–. Curious fact: the 27 lines on a smooth cubic are indeed always distinct. If one allows the surface to have isolated rational double points, then the number is always strictly smaller, but there is a "natural" way to assign a multiplicity to each line such that the sum of the multiplicities is. ~~Around the History of the Twenty-seven Lines upon Cubic. Applied Mathematics 18,89–96. Henderson,Archibald1911.The Twenty-Seven Lines upon the Cubic Surface.NewYork:. of the Lines upon the Surface”. In: The Quarterly Journal of Mathematics 2, 55–65, 110–120.~~

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