Bitangents of tropical plane quartic curves

Abstract

We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic.

13 pages, 9 figures. Minor revisions; accepted for publication in Mathematische Zeitschrift

References in corpus (1)

• Theta characteristics of tropical $K_4$-curves

Cited by in corpus (11)

• Moduli of Tropical Plane Curves
• Lifting tropical bitangents
• Tropicalization of theta characteristics, double covers, and Prym varieties
• Embeddings and immersions of tropical curves
• Tritangent planes to space sextics: the algebraic and tropical stories
• 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
• Avoidance loci and tropicalizations of real bitangents to plane quartics