A tropical construction of a family of real reducible curves

TL;DR

This paper presents a tropical geometric method to construct real algebraic plane curves with many even ovals, demonstrating a new approach to understanding their topology.

Contribution

It introduces a tropical modification technique to construct a family of real reducible curves with asymptotically maximal even ovals, advancing the combinatorial understanding of real algebraic curves.

Findings

Constructive proof of existence of real algebraic curves with many even ovals

Use of tropical modifications in algebraic geometry

Demonstration of asymptotically maximal number of even ovals

Abstract

We give a constructive proof using tropical modifications of the existence of a family of real algebraic plane curves with asymptotically maximal numbers of even ovals.