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On the equality of de Rham depth and formal grade in characteristic zero

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Majid Eghbali

Commutative Algebra · Submitted 20 Jun 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that in this case, the de Rham depth of $Y$ is the same as the so-called formal grade of $I$ in $R$.

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arXiv ID2106.10702 (version 1)
Pith IDH5TGRPOL, Pith's permanent record of this paper and its review
CitationMajid Eghbali. "On the equality of de Rham depth and formal grade in characteristic zero." arXiv:2106.10702 (2021). https://pith.science/paper/H5TGRPOL
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,396 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Let $Y \subset \mathbb{P}^n_k$ be a non-singular proper closed subset of projective $n$-space over a field $k$ of characteristic zero and let $I \subset R=k[x_0, \ldots, x_n]$ be the homogeneous defining ideal of $Y$. We show that in this case, the de Rham depth of $Y$ is the same as the so-called formal grade of $I$ in $R$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Let $Y \subset \mathbb{P}^n_k$ be a non-singular proper closed subset of projective $n$-space over a field $k$ of characteristic zero and let $I \subset R=k[x_0, \ldots, x_n]$ be the homogeneous defining ideal of $Y$. background 0.99 0.07 0.03 unclear 0.58
s1 We show that in this case, the de Rham depth of $Y$ is the same as the so-called formal grade of $I$ in $R$. result 0.99 0.96 0.97 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Let $Y \subset \mathbb{P}^n_k$ be a non-singular proper closed subset of projective $n$-space over a field $k$ of characteristic zero and let $I \subset R=k[x_0, \ldots, x_n]$ be the homogeneous defining ideal of $Y$. We show that in this case, the de Rham depth of $Y$ is the same as the so-called formal grade of $I$ in $R$.

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