The Tropical Three Conics Theorem

"In classical algebraic geometry, the three conics theorem states: given three projective conics that pass through two given points, the three lines joining the other two intersections of each pair of conics all intersect at a point. We identify and prove a tropical three conics theorem when the conics are smooth and intersections are transverse, developing a geometric classification of when five points on a conic uniquely determine it in the process. We then relax our assumptions to allow for non-smooth conics or non-transverse intersections, proving the theorem in more general cases. In particular, one of these general cases implies a tropical version of Pappus' hexagon theorem."