Planar tropical caustics: trivalency and convexity
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916983868489728 |
|---|---|
| author | Shkolnikov, Mikhail |
| author_facet | Shkolnikov, Mikhail |
| contents | 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 possibility of relaxing the convexity condition for the domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Planar tropical caustics: trivalency and convexity Shkolnikov, Mikhail Algebraic Geometry Combinatorics Metric Geometry Number Theory Symplectic Geometry 14T05 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 possibility of relaxing the convexity condition for the domain. |
| title | Planar tropical caustics: trivalency and convexity |
| topic | Algebraic Geometry Combinatorics Metric Geometry Number Theory Symplectic Geometry 14T05 |
| url | https://arxiv.org/abs/2503.11137 |