Maximally inflected real trigonal curves on Hirzebruch surfaces

Abstract

In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base B B of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for B = P 1 B=\mathbb {P}^1 obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over B = P 1 B=\mathbb {P}^1 .