| 释义 |
Kummer SurfaceThe Kummer surfaces are a family of Quartic Surfaces given by the algebraic equation
 | (1) |
 | (2) |
 ,  ,  , and  are the Tetrahedral Coordinates
and  is a parameter which, in the above plots, is set to  . The above plots correspond to 
 | (7) |
 | (8) |
 , 
 | (9) |
 corresponds to four real points.
The following table gives the number of Ordinary Double Points for various ranges of  ,corresponding to the preceding illustrations.
The Kummer surfaces can be represented parametrically by hyperelliptic Theta Functions. Most of theKummer surfaces admit 16 Ordinary Double Points, the maximum possible for a QuarticSurface. A special case of a Kummer surface is the Tetrahedroid.
Nordstrand gives the implicit equations as
 | (10) |
 | (11) |
References
Endraß, S. ``Flächen mit vielen Doppelpunkten.'' DMV-Mitteilungen 4, 17-20, Apr. 1995.Endraß, S. ``Kummer Surfaces.''http://www.mathematik.uni-mainz.de/AlgebraischeGeometrie/docs/Ekummer.shtml. Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, pp. 14-19, 1986. Fischer, G. (Ed.). Plates 34-37 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 33-37, 1986. Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 183, 1994. Hudson, R. Kummer's Quartic Surface. Cambridge, England: Cambridge University Press, 1990. Kummer, E. ``Über die Flächen vierten Grades mit sechszehn singulären Punkten.'' Ges. Werke 2, 418-432. Kummer, E. ``Über Strahlensysteme, deren Brennflächen Flächen vierten Grades mit sechszehn singulären Punkten sind.'' Ges. Werke 2, 418-432. Nordstrand, T. ``Kummer's Surface.'' http://www.uib.no/people/nfytn/kummtxt.htm.
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