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Results tagged with tropical-geometry
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For questions about tropical geometry, piece-wise linear functions with integer slopes, tropical degenerations and applications of tropical geometry, max-plus algebra, and tropical semifields.
2
votes
Gradient of Ronkin function
For your particular function $P$, the gradient of the Ronkin function can be computed explicitly. There are three easy cases: If $e^x+e^y < 1$, then $\nabla R = (0,0)$; if $e^x > e^y+1$ then $\nabla R …
- 156k
1
vote
Accepted
Boundary of a tropical variety.
First of all, $\mathrm{Trop}(X)$ is a set which can be equipped with the structure of a polyhedral complex; there is not a canonical way to do it. However, there are better and worse choices. In parti …
- 156k
4
votes
What can we say about tropical maps $\mathbb{P}^1 \to A$ for an Abelian variety $A$?
The answer should be that there are no non-constant maps from tropical curves of genus zero to tropical abelian varieties. By "should" I mean that there are a lot of definitions of these things in the …
- 156k
8
votes
Weight filtration and Hodge theory for tropical varieties
Itenberg, Kazarkov, Mikhalkin and Zharkov have formulated a definition of tropical $H^{p,q}$. You can read about it in this preprint.
Their definition is restricted to the case that $\mathrm{Trop} \ …
- 156k
11
votes
Accepted
Is there a tropical geometric proof for counting genus g curves in any n dimensional project...
Here is an attempt at an overview of tropical curve counts by someone who has been involved in the story for a while but certainly hasn't followed everything that has happened. I look forward to being …
- 156k