| 释义 |
DervishA Quintic Surface having the maximum possible number of Ordinary Double Points (31),which was constructed by W. Barth in 1994 (Endraß). The implicit equation of the surface is where  is a parameter (Endraß). The surface can also be described by the equation
 | (2) |
 | (3) |
 | (9) |
(Nordstrand).
The dervish is invariant under the Group  and contains exactly 15 lines. Five of these are the intersection ofthe surface with a -invariant cone containing 16 nodes, five are the intersection of the surface with a -invariantplane containing 10 nodes, and the last five are the intersection of the surface with a second -invariant planecontaining no nodes (Endraß).
References
Endraß, S. ``Togliatti Surfaces.''http://www.mathematik.uni-mainz.de/AlgebraischeGeometrie/docs/Etogliatti.shtml.Endraß, S. ``Flächen mit vielen Doppelpunkten.'' DMV-Mitteilungen 4, 17-20, 4/1995. Endraß, S. Symmetrische Fläche mit vielen gewöhnlichen Doppelpunkten. Ph.D. thesis. Erlangen, Germany, 1996. Nordstrand, T. ``Dervish.'' http://www.uib.no/people/nfytn/dervtxt.htm.
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