6 papers
Layered mixed matrices and reaction networks
Arne Kuhrs, Máté L. Telek, Nicola Vassena
The purpose of this work is twofold. In the first part, we consider layered mixed matrices introduced by Murota, relate them to existing notions in combinatorial commutative algebr…
On Bands and Limit Theorems in Tropical Geometry
Arne Kuhrs, Alejandro Martínez Méndez, Pedro Souza
We review the basic theory of bands and band schemes introduced by Baker-Jin-Lorscheid, which is an algebraic framework for tropicalization, analytification, and -geo…
Scheme theory for commutative semirings
Roberto Gualdi, Arne Kuhrs, Mayo Mayo Garcia +1
In this survey, we describe two different approaches to constructing affine schemes for commutative semirings: one based on prime ideals, and another based on prime kernels (also c…
Tropical reductive groups and principal bundles on metric graphs
Andreas Gross, Arne Kuhrs, Martin Ulirsch +1
We propose an elementary tropical analogue of a reductive group that combines the datum of a Weyl group and the tropicalization of a fixed maximal torus. For the classical groups,…
The Signed Goldman-Iwahori Space and Real Tropical Linear Spaces
Kevin Kuehn, Arne Kuhrs
For a real closed field with a non-Archimedean absolute value, we introduce the signed Goldman--Iwahori space, the space of homothety classes of signed seminorms on a finite-di…
Buildings, valuated matroids, and tropical linear spaces
Luca Battistella, Kevin Kuehn, Arne Kuhrs +2
Affine Bruhat--Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of parametrizes flags of subspaces/lattices in or,…