Tritangent planes to space sextics: the algebraic and tropical stories
arXiv:1701.02353 · doi:10.1007/978-1-4939-7486-3_3
Abstract
We discuss the classical problem of counting planes tangent to general canonical sextic curves at three points. We determine the number of real tritangents when such a curve is real. We then revisit a curve constructed by Emch with the greatest known number of real tritangents, and conversely construct a curve with very few real tritangents. Using recent results on the relation between algebraic and tropical theta characteristics, we show that the tropicalization of a canonical sextic curve has 15 tritangent planes.