Timeline for Relation between the index of (the sum of) lattices in euclidean space, and their orthogonal complement.
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Apr 10, 2013 at 15:10 | history | edited | edwold | CC BY-SA 3.0 |
Added an example, fixed link.
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| Apr 9, 2013 at 13:52 | comment | added | edwold | I think they are working, in the article mentioned, with the definition that if $L$ is not a full rank sublattice of $\mathbb{Z}^n$ then the index $[\mathbb{Z}^n:L]$ is by definition equal to $[affine(L) \cap \mathbb{Z}^n:L]$. However, I might be wrong since they do not explicitly state this, but I think this is the only thing that makes sense from the toric-goemetry perspective. | |
| Apr 9, 2013 at 12:52 | comment | added | Roland Bacher | If $V,W$ are $1-$dimensional (linearly independant) and $n\geq 3$ then the index of $M+M'$ (being or rank $2$) is infinite while $L+L'$ has finite index. I guess you want perhaps also $V+W$ and $V^\perp+W^\perp$ to be of full dimension $n$. | |
| Apr 9, 2013 at 11:00 | history | asked | edwold | CC BY-SA 3.0 |