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Feb 7, 2021 at 11:48 comment added Zach Teitler No, I don't know. Writing a polynomial as a sum of products of linear forms is called a Chow decomposition (or other similar names), and in this case it is a sort of special, restricted Chow decomposition (where each term is the product of 6 out of 7 forms). I don't know the results on uniqueness ("identifiability") of Chow decompositions in general, or these special ones.
Feb 7, 2021 at 10:49 comment added user61586 Thank you very much for your answer. Do you know if it is possible to construct a curve $C'$ containing the same star configuration of $C$ without knowing the star configuration explicitly?
Feb 7, 2021 at 10:46 vote accept CommunityBot
Feb 4, 2021 at 7:45 history answered Zach Teitler CC BY-SA 4.0