21 citations · 24 across the 17 of their papers we have counts for
8 papers · 1 filter
Geometric classification of primes modulo a (bend) congruence
Netanel Friedenberg, Kalina Mincheva
In this paper we continue the program to develop the algebraic foundations of tropical (algebraic) geometry. We give strong characterizations of prime congruences containing a give…
Varieties of prime tropical ideals and the dimension of the coordinate semiring
Dániel Joó, Kalina Mincheva
In this note we study the relationship between ideals and congruences of the tropical polynomial and Laurent polynomial semirings. We show that the variety of a non-zero prime idea…
Equivariant vector bundles on toric schemes over semirings
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric ve…
Geometric interpretation of valuated term (pre)orders
Netanel Friedenberg, Kalina Mincheva
Valuated term orders are studied for the purposes of Gröbner theory over fields with valuation. The points of a usual tropical variety correspond to certain valuated terms preorder…
Tropical adic spaces I: The continuous spectrum of a topological semiring
Netanel Friedenberg, Kalina Mincheva
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a t…
Vector bundles on tropical schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
We define vector bundles for tropical schemes, and explore their properties. The paper largely consists of three parts; (1) we study free modules over zero-sum free semirings, whic…
Picard groups for tropical toric schemes
Jaiung Jun, Kalina Mincheva, Jeffrey Tolliver
From any monoid scheme (also known as an -scheme) one can pass to a semiring scheme (a generalization of a tropical scheme) by scalar extension to an idempo…
Computing toric degenerations of flag varieties
Lara Bossinger, Sara Lamboglia, Kalina Mincheva +1
We compute toric degenerations arising from the tropicalization of the full flag varieties and embedded in a product of Grassmannians. For $…