Timeline for What is the combinatorial data classifying non-normal affine toric varieties?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2021 at 17:19 | answer | added | Sergio GGG | timeline score: 2 | |
| Apr 14, 2016 at 2:33 | answer | added | Lev Borisov | timeline score: 2 | |
| Mar 25, 2014 at 21:34 | comment | added | Benjamin Steinberg | The answer maybe there is no answer. I was hoping for an answer not using monoids. | |
| Mar 25, 2014 at 16:41 | comment | added | Allen Knutson | There's even a game exploiting this difficulty: en.wikipedia.org/wiki/Sylver_coinage | |
| Mar 25, 2014 at 16:31 | comment | added | Piotr Achinger | (cont.) Note that any finite set of positive integers generates such a $P\subseteq \mathbb{N}$, but it's quite difficult to see whether two such sets generate the same monoid (see "Frobenius problem"). | |
| Mar 25, 2014 at 16:28 | comment | added | Piotr Achinger | Take a (rational polyhedral) cone $\sigma$ in $\mathbb{R}^n$ and remove a finite number of non-invertible elements of $P:=\sigma\cap \mathbb{Z}^n$. If the resulting $P'$ is a monoid (and if there are no invertible elements, you can make $P'$ a monoid by removing finitely many more elements), it gives you a non-normal affine toric variety, and all not necessarily normal affine toric varieties arise this way. I guess that pairs (cone, finite subset of integral points) is not what you're looking for. What answer would you like to have in case $P\subseteq \mathbb{N}$? | |
| Mar 25, 2014 at 13:40 | history | asked | Benjamin Steinberg | CC BY-SA 3.0 |