For questions related to tropical geometry.

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Significance of eigen vectors in Max-Plus algebra

In Max-Plus algebra we have notion of eigen values and eigen vectors. Given a matrix $A \in \mathbb{R}_{max}^{n\times n}$ , $\mu$ is an eigen value of $A$ if it satisfies $A \otimes v = \mu \otimes v$ ...
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How Max plus algebra is different from conventional algebra?

Here I have some basic questions about max-plus algebra. How this is useful? Why we need to define a different algebra? What aspects are highlighted in this which were untouched in conventional ...
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Operations in Max-Plus Algebra

I am a undergraduate student. I am doing a project on tropical geometry and Max-Plus Algebra. So I started reading about max plus algebra. First thing I came across is that here we don't use ...
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Is the residue field of an algebraically closed field with respect to a non-trivial valuation infinite?

Let $K$ be an algebraically closed field with a non-trivial valuation. Let $\Bbb k$ be the residue field, i.e. $\Bbb k = R/\mathfrak m$ where $R$ is the valuation ring $R:=\{a\in K\mid \text{val} ...
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Gradient of Ronkin function

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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Motivation for the study of amoebas.

What was the primary motivation for the study of the amoebas?
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Tropical versus max-plus

Is the max-plus algebra an example of tropical mathematics or is it an independent structure? How can we turn a max-plus algebra into tropical geometry or viceversa-if possible?
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What is the link of the origin of a polyhedral fan?

I am trying to understand the article http://arxiv.org/abs/0804.3651 by David Helm and Eric Katz. There the link of the origin of a polyhedral fan is mentioned. I googled and only found definitions ...
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Transition functions of toric projective bundle (Proposition in [Cox, Toric Varieties])

My reference: David Cox's "Toric Varieties" My question is the proof of Proposition 7.3.3. Proposition 7.3.3. The cones {$\sigma_i$ | $\sigma \in \Sigma$, $i = 0,\dots,r$} and their faces form ...
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Tropical Machinery

Recently I heard of a recent field in mathematics called tropical geometry. Having read the wiki page on it it seems like it is combinatorial algebraic geometry. My question is what are the benefits ...
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The structure theorem of Tropical geometry

The Structure Theorem of Tropical geometry states that "Let $X$ be an irreducible $d$-dimensional subvariety of $\mathbb T^n$ . Then $\operatorname{trop}(X)$ is the support of a balanced weighted ...