For each homogeneous ideal I the paper defines a point configuration A(I); the regular subdivisions of A(I) provide two ideals between which every initial ideal in_w I must lie, and these bounds are categorical limits.
The Grassmannian of 3-planes in C8 is sch¨ on.Algebraic Combina- torics, 6(5):1273–1299, 2023
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Regular subdivisions, bounds on initial ideals, and categorical limits
For each homogeneous ideal I the paper defines a point configuration A(I); the regular subdivisions of A(I) provide two ideals between which every initial ideal in_w I must lie, and these bounds are categorical limits.