Lie’s double translation surfaces meet theta surfaces
- Türkü Özlüm Celik (University of Leipzig)
A theta surface in affine 3-space is the zero set of a Riemann theta function. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincaré showed that theta surfaces are precisely the surfaces of double translation, i.e. obtained as the Minkowski sum of two space curves in two different ways. These curves are parametrized by abelian integrals, so they are usually not algebraic. This is joint work with Daniele Agostini, Julia Struwe and Bernd Sturmfels which offers a new view on this classical topic through the lens of computation.