https://arxiv.org/pdf/1702.04862.pdf

# CubicCover

Steve Trettel

Medium | Mathematica notebook. |
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The Art | The orientation double cover of a real cubic surface in projective 3-space, embedded in the 3-sphere. In this case, the resulting surface has genus 6, and is animated as a variety of projective transformations are applied. |

The Math | A cubic surface is the blow up of projective 2-space at 6 points. As blowing up a real 2-dimensional surface is topologically equivalent to cutting out a disk and sewing in a Mobius band, the set of real points of a cubic surface determines a non-orientable surface, and its particular topology depends on the number of real lines it contains. Taking the orientation cover replaces this an orientable surface, of genus 6 if all lines are real. |

Categories | Algebraic Geometry, Math Illustration, Projective Geometry |