Dervish

A 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

	(1)

(2)

(3)

			(4)
			(5)
			(6)
			(7)
			(8)

(9)

			(10)
			(11)
			(12)

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.

• Persistent Number
• Persistent Process
• Perspective
• Perspective Axis
• Perspective Center
• Perspective Collineation
• Perspective Triangles
• Perspectivity
• Pesin Theory
• Petersen Graphs
• Petersen-Shoute Theorem
• Peters Projection
• Peter-Weyl Theorem
• Petrie Polygon
• Petrov Notation
• Pfaffian Form
• p-Good Path
• p-Group
• Phase
• Phase Space
• Phase Transition
• Phasor
• Phi Curve
• Phi Number System
• Phragmén-Lindêlöf Theorem