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etale projection of the tropicalization

Let $(K,v)$ be a complete valued field with value group $\mathbb R$, and let $X$ be a closed subvariety of dimension $d$ of the algebraic torus $(K^\times)^n$. Let $\sigma$ be a polyhedron in the ...
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group structure on (subsets of) tropicalizations of Abelian varieties

In this paper Vigeland shows how one can define a group law on subset of a tropical elliptic curve, so that this group is homeomorphic to $S^1$. It is not clear to me what is the relationship between ...
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Can Hausdorff dimension make sets into a Tropical Semiring?

If $X$ is a metric space, we construct Hausdorff $d$ measure from the outer measure H^d(U) = \lim_{\delta \to 0}\inf\left\{\sum_{i=1}^\infty \left(\text{diam}(E_i)\right)^d : \...
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Boundary of a tropical variety.

For a variety X (over some proper fields), if Trop(X) is a tropicalization of X, then we know that Trop(X) is a polyhedral complex. If we consider the interior of the support of that polyhedral ...
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Has this generalization of a determinant (assigning multiplicities to the rows) been studied?

I'm working on some questions in tropical geometry, and my problem led me to create the following generalization of a determinant: Let $A$ be an $m \times n$ matrix with $m \le n$, and positive ...
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I have a complex curve $P(z,w)=z+w-1=0$. I get the amoeba map $$(z,w)\rightarrow (\log|z|,\log|w|)$$ of this curve. It's look like this http://en.wikipedia.org/wiki/Amoeba_(mathematics) (the first ...
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Volume in tropical geometry as compared to volume in convex geometry

In tropical geometry, is there a notion of volume. Maybe one with some of the properties as found in classical convex geometry? If so, is there a good reference that elaborates on this question. I ...
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What is Tropicalization, and how is it applied

My question is: What is Tropicalization, how is it done, and what are some basic applications of it? motivation I am interested especially in how questions about enumerative algebraic geometry ...
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$L_1$ and $L_\infty$ Voronoi diagrams and tropical geometry: Connection?

I just realized that there is a visual similarity between Voronoi diagrams in the $L_1$ and $L_\infty$ metrics (two images below)     Left: O'Rourke, "Computing Relative Neighborhood graph ...
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Chow ring of extended tropicalizations

In Allermann-Rau '09, the authors define the Chow groups of an arbitrary abstract tropical cycle. In particular, one may take the tropical cycle to be the tropicalization of a subvariety of a torus. ...
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Tropical homological algebra

Has anyone out there thought about homological algebra over the tropical semifield $\mathbb{T}$? For example, I'm interested in the Hochschild homology and cyclic homology of tropical algebras, if ...
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When is the quotient of a tropical curve also a tropical curve?

A plane tropical curve $\Gamma$ is the corner locus of a tropical polynomial in two variables. That is, it is the set of points at which the tropical polynomial, which is a piecewise-linear concave ...
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What can we learn from the tropicalization of an algebraic variety?

I often hear people speaking of the many connections between algebraic varieties and tropical geometry and how geometric information about a variety can be read off from the associated tropical ...
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Weight filtration and Hodge theory for tropical varieties

Many concepts is algebraic geometry have tropical analogues. Question: Is there an analogue of the weight filtration or Hodge filtration for tropical varieties? A tropical curve ends up being ...
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How to Tropicalize a Polynomial in Two Variables?

Trying to draw the Amoeba With Mathematica, it's possible to graph $e^{-k x} + e^{-k y} = 1,e^{-k x} - e^{-k y} = 1$ and $e^{-k x} + e^{-k y} = -1$ to get the amoeba of 1 + x + y when k = 1. Then by ...
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Tropical varieties correspondence to varieties over a non-archimedean valuation field.

I am a mathematical physicist and I am studying certain discrete dynamical systems defined in terms of piecewise linear mappings, which may be expressed in terms of expressions over the max-plus semi-...
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Simple topological question on taking complements inside a simplex

We would like to know if the following claim is true: (If you don't know the definition of a tropical hyperplane, then please consider the case when d=3) Let $P_1,\cdots,P_d$ be full dimensional (...
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Is anything known about the enumeration of degree d, genus g curves in CP^2 where g >1 ?

I wanted to know if there is something analogous to Kontsevich's recursion formula for enumeration of genus zero curves in $\mathbb{C}\mathbb{P}^2$, for higher genus curves. There is a similar ...