Repairing tropicalizations of plane curves with modifications

In tropical geometry, algebraic varieties are degenerated to polyhedral complexes, so-called tropical varieties. The fact that a tropical variety still reflects many properties of the degenerated variety allows an infusion of polyhedral and combinatorial methods into algebraic geometry. Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. In this talk, we present tropical modi cations as a tool to locally repair bad embeddings of plane curves, allowing the re-embedded tropical curve to better reflect the geometry of the input curve. Joint work with Angelica Cueto.