Real Tropical Quartics and their Bitangents: Counting with Patchworking

Abstract

For certain tropical quartic curves the existing techniques could not predict the lifting behavior of their bitangents over the real numbers. We close this gap by using patchworking techniques. Further, this paper provides an analysis of the combinatorial types of real tropical quartic curves according to their real topology and number of real bitangents. This paper is accompanied by an extension for polymake; the computational data is available in the database collection polyDB.