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Bitangents of tropical plane quartic curves. (English) Zbl 1371.14067
Summary: 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.

MSC:
14T05 Tropical geometry (MSC2010)
14H45 Special algebraic curves and curves of low genus
14H50 Plane and space curves
14H51 Special divisors on curves (gonality, Brill-Noether theory)
Software:
TOPCOM
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