TOPICS
Search

Hauser's Helix Surface

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
Hauser's helix surface

Hauser's helix surface is the quartic surface

6x^2-2x^4=y^2z^2,

called "Helix" in Hauser's gallery. It is distinct from a helix, which is a space curve. Its singular points form the z-axis and the y-axis. The equation is unchanged by reversing the sign of any coordinate or interchanging y and z.

After scaling the coordinates, the equation becomes

X^4+Y^2Z^2=X^2.

Faber and Hauser (2010, pp. 393-399) use this form to compare methods of resolution of singularities and to illustrate the role of symmetry in the choice of blow-up centers.

See also

Algebraic Blow-Up, Quartic Surface, Resolution of Singularities

Explore with Wolfram|Alpha

References

Faber, E. and Hauser, H. "Today's Menu: Geometry and Resolution of Singular Algebraic Surfaces." Bull. Amer. Math. Soc. 47, 373-417, 2010. https://doi.org/10.1090/S0273-0979-10-01295-4.Hauser, H. "Gallery of Singular Algebraic Surfaces: Helix." https://homepage.univie.ac.at/herwig.hauser/gallery.html.

Cite this as:

Weisstein, Eric W. "Hauser's Helix Surface." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HausersHelixSurface.html

Subject classifications