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

# EllipticSurface2

Steve Trettel

Medium | Mathematica notebook. |
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The Art | A real cubic surface together with a singular foliation by real elliptic curves, animated as the curves trace out the surface. |

The Math | Elliptically fibered surfaces are 2 dimensional algebraic varieties with a map to a 1-dimensional curve, whose preimages are generically elliptic curves. The full theory applies to the complex case, where such a surface is a real 4-manifold foliated by tori and their degenerations, though with a careful choice of surface much of the geometry reamins visible in the set of real points. |

Categories | Algebraic Geometry, Math Illustration |