Canonical Hilbert-Burch matrices for ideals of k[x,y]
classification
🧮 math.AC
math.AG
keywords
canonicalhilbert-burchmatricesaffineapplicationartinianbetticells
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An Artinian ideal $I$ of $k[x,y]$ has many Hilbert-Burch matrices. We show that there is a canonical choice. As an application, we determine the dimension of certain affine Gr\"obner cells and their Betti strata recovering results of Ellingsrud and Str{\o}mme, G\"ottsche and Iarrobino.
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