Related papers: Finitely generated congruences on tropical rationa…

An unconstrained optimization problem is formulated in terms of tropical mathematics to minimize a functional that is defined on a vector set by a matrix and calculated through multiplicative conjugate transposition. For some particular…

We study whether a given tropical curve $\Gamma$ in $\mathbb{R}^n$ can be realized as the tropicalization of an algebraic curve whose non-archimedean skeleton is faithfully represented by $\Gamma$. We give an affirmative answer to this…

In this paper, we prove that: For any given finitely many distinct points $P_1,...,P_r$ and a closed subvariety $S$ of codimension $\geq 2$ in a complete toric variety over a uncountable (characteristic 0) algebraically closed field, there…

A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the…

In this paper we present two intrinsic algebraic definitions of tropical variety motivated by the classical Zariski correspondence, one utilizing the algebraic structure of the coordinate semiring of an affine supertropical algebraic set,…

We introduce the notion of resultant of two planar curves in the tropical geometry framework. We prove that the tropicalization of the algebraic resultant can be used to compute the stable intersection of two tropical plane curves. It is…

In this paper we give an interpretation to the boundary points of the compactification of the parameter space of convex projective structures on an n-manifold M. These spaces are closed semi-algebraic subsets of the variety of characters of…

We consider tropical hemispaces, defined as tropically convex sets whose complements are also tropically convex, and tropical semispaces, defined as maximal tropically convex sets not containing a given point. We introduce the concept of…

We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest…

Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M, we conjecture that if the Tate cohomology $\HHHH^*(G, M)$ of G with coefficients in M is finitely…

In tropical geometry, given a curve in a toric variety, one defines a corresponding graph embedded in Euclidean space. We study the problem of reversing this process for curves of genus zero and one. Our methods focus on describing curves…

Let R be a class of groups closed under taking semidirect products with finite kernel and fully residually R-groups. We prove that R contains all R-by-{finitely generated residually finite} groups. It follows that a semidirect product of a…

We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the…

In this paper, we provide an equivalent condition for the Chvatal-Gomory (CG) closure of a closed convex set to be finitely-generated. Using this result, we are able to prove that, for any closed convex set that can be written as the…

Let $T$ be a compact torus. We prove that, up to equivariant rational equivalence, the category of $T$-simply connected, $T$-finite type $T$-spaces with finitely many isotropy types is completely described by certain finite systems of…

A key issue in tropical geometry is the lifting of intersection points to a non-Archimedean field. Here, we ask: Where can classical intersection points of planar curves tropicalize to? An answer should have two parts: first, identifying…

Using ideas from the theory of tropical curves and degeneration, we prove that any Fano hypersurface (and more generally Fano complete intersections) is swept by at most quadratic rational curves.

Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…

We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine…

We begin by defining general hypergeometric functions over finite fields and obtaining a finite field analogue of a classical symmetry in their complex counterparts. We give a geometric proof for the symmetry by constructing isomorphisms…