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Tülle Surface


tuelle surface

The tülle surface is the quartic surface

 yz(x^2+y-z)=0,

named by Hauser. Its German name Tülle means "nozzle." It is the union of the two planes y=0 and z=0 and the parabolic cylinder z=x^2+y.

The pairwise intersections of these three smooth components are the x-axis and the two parabolas y=0, z=x^2 and z=0, y=-x^2. All three curves have the same tangent line at the origin. Although each pair of components meets transversally, the three tangent planes at the origin have linearly dependent normals. Thus this union is not a simple normal crossing divisor.


See also

Parabolic Cylinder, Quartic Surface, Simple Normal Crossing Divisor

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References

Hauser, H. "Gallery of Singular Algebraic Surfaces: Tuelle." https://homepage.univie.ac.at/herwig.hauser/gallery.html.

Cite this as:

Weisstein, Eric W. "Tülle Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TuelleSurface.html

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