Lifting tropical bitangents. (January 2020)

• Record Type: Journal Article
• Authors: Len, Yoav; Markwig, Hannah
• Is Part Of: Journal of symbolic computation. Volume 96(2020)
• Page Start: 122
• Page End: 152
• Publication Date: 2020-01
• Subjects: 14T05; Tropical geometry -- Bitangents of quartics; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.015
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We study lifts of tropical bitangents to the tropicalization of a given complex algebraic curve together with their lifting multiplicities. Using this characterization, we show that generically all the seven bitangents of a smooth tropical plane quartic lift in sets of four to algebraic bitangents. We do this constructively, i.e. we give solutions for the initial terms of the coefficients of the bitangent lines. This is a step towards a tropical proof that a general smooth quartic admits 28 bitangent lines. The methods are also appropriate to count real bitangents; however the conditions to determine whether a tropical bitangent has real lifts are not purely combinatorial.