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- W4287639295 abstract "Given an affine algebra $R=P/I$, where $P=K[x_1,dots,x_n]$ is a polynomial ring over a field $K$ and $I$ is an ideal in $P$, we study re-embeddings of the affine scheme ${rm Spec}(R)$, i.e., presentations $R cong P'/I'$ such that $P'$ is a polynomial ring in fewer indeterminates. To find such re-embeddings, we use polynomials $f_i$ in the ideal $I$ which are coherently separating in the sense that they are of the form $f_i= z_i - g_i$ with an indeterminate $z_i$ which divides neither a term in the support of $g_i$ nor in the support of $f_j$ for $jne i$. The possible numbers of such sets of polynomials are shown to be governed by the Grobner fan of $I$. The dimension of the cotangent space of $R$ at a $K$-linear maximal ideal is a lower bound for the embedding dimension, and if we find coherently separating polynomials corresponding to this bound, we know that we have determined the embedding dimension of $R$ and found an optimal re-embedding." @default.
- W4287639295 created "2022-07-25" @default.
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- W4287639295 date "2020-10-16" @default.
- W4287639295 modified "2023-09-25" @default.
- W4287639295 title "Cotangent spaces and separating re-embeddings" @default.
- W4287639295 doi "https://doi.org/10.48550/arxiv.2010.08378" @default.
- W4287639295 hasPublicationYear "2020" @default.
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