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Aug 8, 2017 at 1:29 comment added Jeanne Clelland Robert, thanks so much! I'll have to think about this. The big problem is that I know almost nothing about the functions $c_{j_0 j_1 j_2 j_3}(\lambda)$, because they themselves are expressed in terms of three unknown functions of $\lambda$ and their derivatives up to order 2. Ultimately I want to know necessary conditions on these 3 unknown functions of $\lambda$ for the zero locus $Z$ you describe above to have dimension at least 1.
Aug 7, 2017 at 21:43 history answered Robert Bryant CC BY-SA 3.0