Tropical Quadrics Through Three Points

TL;DR

This paper studies tropical quadrics passing through three points, analyzing their structure within tropical geometry, and explores related tropical Grassmannians and a small tropical Hilbert scheme.

Contribution

It characterizes the tropicalization of quadrics through three points and identifies these within the tropical Grassmannian, introducing a small tropical Hilbert scheme.

Findings

The tropicalization of the map is contained in the tropicalization of its image.

Identified objects inside the tropical Grassmannian of planes in projective 5-space.

Explored a small tropical Hilbert scheme.

Abstract

We tropicalize the rational map that takes triples of points in the projective plane to the plane of quadrics passing through these points. The image of its tropicalization is contained in the tropicalization of its image. We identify these objects inside the tropical Grassmannian of planes in projective 5-space, and we explore a small tropical Hilbert scheme.