1 citations · 1 across the 3 of their papers we have counts for
3 papers
math.AG2023
Geometry of tropical extensions of hyperfields
James Maxwell, Ben Smith
We study the geometry of tropical extensions of hyperfields, including the ordinary, signed and complex tropical hyperfields. We introduce the framework of 'enriched valuations' as…
math.MG2023
Convex geometry over ordered hyperfields
James Maxwell, Ben Smith
We initiate the study of convex geometry over ordered hyperfields. We define convex sets and halfspaces over ordered hyperfields, presenting structure theorems over hyperfields ari…
math.AG2021★ 1 cited
Generalising Kapranov's Theorem For Tropical Geometry Over Hyperfields
James Maxwell
Kapranov's theorem is a foundational result in tropical geometry. It states that the set of tropicalisations of points on a hypersurface coincides precisely with the tropical varie…