http://trdunlap2.wordpress.com What I'm working on and what I'm finding Wed, 08 Jul 2009 18:50:18 +0000 http://wordpress.com/ hourly 1 http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-29 trdunlap2 Thu, 13 Dec 2007 01:16:46 +0000 http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-29 I should say, though, that the equations in Kamnitzer are pulled directly from a paper by Berenstein and Zelevinsky (arXiv:math.RT/9912012) in the "naive" way. So I my impression from S&S may be wrong. I should say, though, that the equations in Kamnitzer are pulled directly from a paper by Berenstein and Zelevinsky (arXiv:math.RT/9912012) in the “naive” way. So I my impression from S&S may be wrong.

]]> http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-28 trdunlap2 Thu, 13 Dec 2007 00:05:49 +0000 http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-28 As for tropicalization, here's a for example. Take $latex x_1\lambda_1-x_2\lambda_2+x_3\lambda_3=0$. If we tropicalize naively by taking valuations then we might get something like: $latex \min\{\tilde{x}_1+\tilde\lambda_1,\tilde{x}_2+\tilde\lambda_2,\tilde{x}_3+\tilde\lambda_3\}\le\infty$ But that's no relation at all. So what we do, and I don't understand the process 100% yet, is consider a different form of the equation. For example: $latex x_1\lambda_1=x_2\lambda_2-x_3\lambda_3$ yields: $latex \tilde x_1+\tilde\lambda_1=\min\{\tilde x_2+\tilde\lambda_2,\tilde x_3+\tilde\lambda_3\}$ This is what I get so far from the Speyer/Sturmfels paper I added to my "sources" page. As for tropicalization, here’s a for example. Take . If we tropicalize naively by taking valuations then we might get something like:

But that’s no relation at all. So what we do, and I don’t understand the process 100% yet, is consider a different form of the equation. For example:

yields:

This is what I get so far from the Speyer/Sturmfels paper I added to my “sources” page.

]]> http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-27 trdunlap2 Wed, 12 Dec 2007 14:37:10 +0000 http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-27 Its seems that tropicalizing a function is very easy but tropicalizing ideals is somewhat subtle. Its seems that tropicalizing a function is very easy but tropicalizing ideals is somewhat subtle.

]]> http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-20 DN Sun, 09 Dec 2007 14:11:37 +0000 http://trdunlap2.wordpress.com/tropical-plucker-relations/#comment-20 I'd really like to understand how these equations are derived. Namely, starting from the ordinary Plucker relations, how does one tropicalize? I’d really like to understand how these equations are derived. Namely, starting from the ordinary Plucker relations, how does one tropicalize?

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