| 释义 |
Clebsch Diagonal CubicA Cubic Algebraic Surface given by the equation
 | (1) |
 | (2) |
 is | |  | (3) |
(Hunt, Nordstrand). On Clebsch's diagonal surface, all 27 of the complex lines (Solomon's Seal Lines) present on ageneral smooth Cubic Surface are real. In addition, there are 10 points on the surface where 3 of the 27 lines meet. These points are called Eckardt Points (Fischer 1986, Hunt), and the Clebsch diagonal surface is theunique Cubic Surface containing 10 such points (Hunt).
If one of the variables describing Clebsch's diagonal surface is dropped, leaving the equations
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 | (5) |
 | (6) |
References
Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, pp. 9-11, 1986.Fischer, G. (Ed.). Plates 10-12 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 13-15, 1986. Hunt, B. The Geometry of Some Special Arithmetic Quotients. New York: Springer-Verlag, pp. 122-128, 1996. Nordstrand, T. ``Clebsch Diagonal Surface.'' http://www.uib.no/people/nfytn/clebtxt.htm.
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