Related papers: Connectivity of tropicalizations

We reveal an algorithm for determining the complete prefix code irreducibility (CPC-irreducibility) of dyadic trees labeled by a finite alphabet. By introducing an extended directed graph representation of tree shift of finite type (TSFT),…

We show that $\mathbb A^1$-connectedness of a large class of varieties over a field $k$ can be characterized as the condition that their generic point can be connected to a $k$-rational point using (not necessarily naive) $\mathbb…

In this article, we study the geometric properties of codimension one foliations on Riemannian manifolds equipped with vector fields that are closed and conformal. Apart from its singularities, these vector fields define codimension one…

Tropicalization is a procedure that assigns polyhedral complexes to algebraic subvarieties of a torus. If one fixes a weighted polyhedral complex, one may study the set of all subvarieties of a toric variety that have that complex as their…

A tropical expansion is a degeneration of a toroidal embedding, induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admits a collapsing map down to a stratum of the original…

We study the tropicalization of intersections of plane curves, under the assumption that they have the same tropicalization. We show that the set of tropical divisors that arise in this manner is a pure dimensional balanced polyhedral…

Some projective wonderful models for the complement of a toric arrangement in a n-dimensional algebraic torus T were constructed in [3]. In this paper we describe their integer cohomology rings by generators and relations.

Let $K$ be a real closed field with a nontrivial non-archimedean absolute value. We study a refined version of the tropicalization map, which we call real tropicalization map, that takes into account the signs on $K$. We study images of…

Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $\Phi:M\to so(3)$. The pair $(A,\Phi)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge…

The category $STROP_m$ of supertropical monoids, whose morphisms are transmissions, has the full--reflective subcategory $STROP$ of commutative semirings. In this setup, quotients are determined directly by equivalence relations, as ideals…

Let A be a basic connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. Under a hypothesis on T, we establish a correspondence…

We consider the Kisin variety associated to a $n$-dimensional absolutely irreducible mod $p$ Galois representation $\bar\rho$ of a $p$-adic field $K$ and a cocharacter $\mu$. Kisin conjectured that the Kisin variety is connected in this…

We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the…

The subject of the present paper is phase tropicalization, which was used crucially in the context of Mikhalkin's correspondence theorem for curve counting in the complex coefficient case. The subject can be traced back to Viro's…

The main purpose of the paper is to establish a closedness theorem over Henselian valued fields $K$ of equicharacteristic zero (not necessarily algebraically closed) with separated analytic structure. It says that every projection with a…

We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field \kk(t_1,\dots,t_d) of rational functions over an…

Suppose $M$ is a closed, connected, orientable, \irr\ \3m\ such that $G=\pi_1(M)$ is infinite. One consequence of Thurston's geometrization conjecture is that the universal covering space $\widetilde{M}$ of $M$ must be \homeo\ to $\RRR$.…

We show that any open 2-dimensional topological field theory valued in a symmetric monoidal $\infty$-category (with suitable colimits) extends canonically to an open-closed field theory whose value at the circle is the Hochschild homology…

Many important problems in extremal combinatorics can be stated as certifying polynomial inequalities in graph homomorphism numbers, and in particular, many ask to certify pure binomial inequalities. For a fixed collection of graphs…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…