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This approach reveals a hypersurface's properties in projective space, indicating advancements in combinatorial techniques.
In the paper we provide a new method of proving the existence of a hypersurface of degree d in Pⁿ, with a general point of multiplicity m and vanishing at a given set of points Z, by looking at weak combinatorics of a set Z. This method has a direct application in the theory of unexpected hypersurfaces, where many of the examples are based only on computer experiments.
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Dumnicki et al. (2025) studied this question.
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