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Vol. 51 No. 1 (2025)
Serdica Mathematical Journal

Articles

Planar tropical caustics: trivalency and convexity

https://doi.org/10.55630/serdica.2025.51.47-72

Published 14-10-2025

  • Mikhail Shkolnikov

Mikhail Shkolnikov
Institute of Mathematics and Informatics, BAS

Abstract

Tropical caustic of a convex domain on the plane is a canonically associated tropical analytic curve inside the domain. In this note we give a graphical proof for the classification of its intermediate vertices, implying in particular that they are always trivalent. Apart from that we explain how various known examples of tropical caustics are constructed and discuss the posibility of relaxing the convexity conditionon for the domain.

2020 Mathematics Subject Classification:

14T20, 11A55, 14M25, 53E50

Keywords

tropical curves, caustics, toric surfaces

Full text

Author Details

Mikhail Shkolnikov

Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Acad. G. Bonchev Str., Bl. 8
1113 Sofia, Bulgaria
e-mail: m.shkolnikov@math.bas.bg

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