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Jan 27, 2020 at 13:39 comment added Magma There's Chern's theorem which could discretize to the desired statement, but it only applies in the case of even $d$.
Jan 27, 2020 at 13:34 comment added M. Winter Thank you. My argument for $d=2$ was exactly along these lines and I hoped to generalize. But I do not know about a higher dimensional analogue of Descartes' theorem.
Jan 27, 2020 at 13:27 history answered Magma CC BY-SA 4.0