Lifting tropical bitangents

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.

35 pages, 24 figures, 1 table. Minor changes. Accepted for publication in Journal of Symbolic Computation

References in corpus (3)

• Lifting harmonic morphisms II: tropical curves and metrized complexes
• Bitangents of tropical plane quartic curves
• Tropical theta characteristics

Cited by in corpus (5)

• Combinatorics and real lifts of bitangents to tropical quartic curves
• Bitangents of non-smooth tropical quartics
• Bitangents to plane quartics via tropical geometry: rationality, ${\mathbb{A}}^1$-enumeration, and real signed count
• Projective duals to algebraic and tropical hypersurfaces
• Hyperbolic plane curves near the non-singular tropical limit