Related papers: Super currents and tropical geometry
We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without…
We present two effective tools for computing the positive tropicalization of algebraic varieties. First, we outline conditions under which the initial ideal can be used to compute the positive tropicalization, offering a real analogue to…
The aim of this paper is to show two applications of metric currents to complex analysis. After recalling the basic definitions, we give a detailed proof of the comparison theorem between metric currents and classical ones on a manifold. In…
In this paper, we study the existence of the tangent cone to a positive plurisubharmonic or plurisuperharmonic current with a suitable condition. Some Estimates of the growth of the Lelong functions associated to the current and to its…
We introduce a notion of super-potential (canonical function) associated to positive closed (p,p)-currents on compact Kaehler manifolds and we develop a calculus on such currents. One of the key points in our study is the use of…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
We study Lelong numbers of currents of full mass intersection on a compact Kaehler manifold in a mixed setting. Our main theorems cover some recent results due to Darvas-Di Nezza-Lu. One of the key ingredients in our approach is a new…
Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case…
We investigate the intersection of positive closed currents in a general setting, employing tangent currents alongside King's residue formula. Our main result establishes a natural condition for the intersection--namely, the Dinh-Sibony…
We consider the class of integer rectifiable currents without boundary satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.
A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to…
Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…
This paper surveys {\it tropical modifications}, which have already become a folklore in tropical geometry. Tropical modifications are used in tropical intersection theory, tropical Hodge theory, and in the study of singularities. They…
Let $\Sigma$ be a closed orientable hyperbolic surface. We introduce the notion of a \textit{geodesic current with corners} on $\Sigma$, which behaves like a geodesic current away from certain singularities (the "corners"). We topologize…
We describe the behaviour at infinity of the bifurcation current in the moduli space of quadratic rational maps. To this purpose, we extend it to some closed, positive (1, 1)-current on a two-dimensional complex projective space and then…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
In this article, we study the order of a positive pluriharmonic current and we compare it with either the order of the concurrent slices or the directionnel orders of the current. Therefore some estimates of the growth of the…
In this study, we first define the local potential associated to a weakly positive closed supercurrent in analogy to the one investigated by Ben Messaoud and El Mir in the complex setting. Next, we study the definition and the continuity of…
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…
We analyse the dynamics of the pullback of the map $z \longmapsto z^m$ on the complex tori and toric varieties. We will observe that tropical objects naturally appear in the limit, and review several theorems in tropical geometry.