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

EllipticSurface3

Steve Trettel

MediumMathematica notebook.
The ArtA real cubic surface together with a singular foliation by real elliptic curves, animated as the curves trace out the surface.
The MathElliptically 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.
CategoriesAlgebraic Geometry, Math Illustration