Related papers: Balancing conditions in global tropical geometry
This paper is devoted to the bounding and computation of the dimension of deformation spaces of tropical curves and hypersurfaces. This characteristic is interesting in light of the fact that it often coincides with the dimension of…
We show how to equip the cone complexes of toroidal embeddings with additional structure that allows to define a balancing condition for weighted subcomplexes. We then proceed to develop the foundations of an intersection theory on cone…
Ultracold atoms provide an ideal system for the realization of quantum technologies, but also for the study of fundamental physical questions such as the emergence of decoherence and classicality in quantum many-body systems. Here, we study…
We perform molecular-dynamics simulations of a molecular system in supercooled states for different values of inertia parameters to provide evidence that the long-time dynamics depends only on the equilibrium structure. This observation is…
We study stability of abstract differential equations coupled by means of a general algebraic condition. Our approach is based on techniques from operator theory and systems theory, and it allows us to study coupled systems by exploiting…
We study integral plane curves meeting at a single unibranch point and show that such curves must satisfy two equivalent conditions. A numeric condition: the local invariants of the curves at the contact point must be arithmetically…
We establish a new notion of tropical convexity for signed tropical numbers. We provide several equivalent descriptions involving balance relations and intersections of open halfspaces as well as the image of a union of polytopes over…
Recently, concepts from the emerging field of tropical geometry have been used to identify different scaling regimes in chemical reaction networks where dimension reduction may take place. In this paper, we try to formalize these ideas…
We reconcile the discrepancy between the complex and tropical counts of some enumerative problems reducing to positive characteristic. Each problem that we consider suggests a prime with special behaviour. Modulo this prime, the solutions…
For a complex hypersurface of dimension $d \geq 1$ in a toric variety, we construct lifts of tropical $(p, q)$-cycles with $p+q=d$ in the associated tropical hypersurface. The tropical cycles we consider are described by Minkowski weights,…
This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population…
In this paper, we consider a new class of generalized Convex structure and we investigate their tropical limits. Some properties are pointing out such that translation homotheticity and others ones allowing to consider the case of discrete…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
A single-column model run under the weak temperature gradient approximation, a parameterization of large-scale dynamics appropriate for the tropical atmosphere, is shown to have multiple stable equilibria. Under conditions permitting…
We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically…
Tyomkin's correspondence theorem states the equality of counts of rational curves of fixed homology class in a toric surface satisfying point and cross-ratio conditions with their tropical counterparts. Such correspondence theorems allow us…
The algebraic foundation of tropical polynomial algebra provides the framework for the geometric construction of the supplement and the reversal of tropical varieties, thereby inducing a duality of reduced tropical varieties; for classes of…
A tropical complete intersection curve C in R^(n+1) is a transversal intersection of n smooth tropical hypersurfaces. We give a formula for the number of vertices of C given by the degrees of the tropical hypersurfaces. We also compute the…
We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry. Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over idempotent semirings such as $\mathbb{T} = (\mathbb{R}\cup…
In this paper we further develop the theory of geometric tropicalization due to Hacking, Keel and Tevelev and we describe tropical methods for implicitization of surfaces. More precisely, we enrich this theory with a combinatorial formula…