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Jul 23, 2017 at 8:25 comment added Dima Pasechnik Right, indeed, in arxiv.org/pdf/0812.1624.pdf the duality I outlined is developed for $m=2$. (My description is incomplete, as at some point one has to take the convex closure of the dual variety). I do not know how much of it can be carried over to the case $m>2$, but I presume at least the general setup can.
Jul 22, 2017 at 22:00 comment added gondolf That is usually called nemerical range for $m=2$.
Jul 21, 2017 at 15:15 comment added Dima Pasechnik I suppose that it's not really known. It will be instructive to start with the first non-trivial case, $m=2$.
Jul 21, 2017 at 0:07 comment added gondolf Thanks! I am particular interested in the polynomial characterization of $S$ with $m=4$. Is there good way to understand it?
Jul 20, 2017 at 12:04 history answered Dima Pasechnik CC BY-SA 3.0