Endraß Octic


Endraß surfaces are a pair of octic surfaces which have 168 ordinary double points. This is the maximum number known to exist for an octic surface, although the rigorous upper bound is 174. The equations of the surfaces X_8^+/- are


where w is a parameter. All ordinary double points of X_8^+ are real, while 24 of those in X_8^- are complex. The surfaces were discovered in a five-dimensional family of octics with 112 nodes, and are invariant under the group D_8×C_2.

The surfaces illustrated above take w=1. The first of these has 144 real ordinary double points, and the second of which has 144 complex ordinary double points, 128 of which are real.

See also

Algebraic Surface, Octic Surface

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Endraß, S. "Octics with 168 Nodes."ß, S. "Flächen mit vielen Doppelpunkten." DMV-Mitteilungen 4, 17-20, 4/1995.Endraß, S. "A Proctive Surface of Degree Eight with 168 Nodes." J. Algebraic Geom. 6, 325-334, 1997.

Cite this as:

Weisstein, Eric W. "Endraß Octic." From MathWorld--A Wolfram Web Resource.

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