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Join operation and ${\mathcal A}$-finite map-germs

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Maria Elenice Rodrigues Hernandes, Maria Aparecida Soares Ruas

Algebraic Geometry · Submitted 11 May 2021

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

The authors' main claim In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{p},0)$ for $p\geq 2n$ of any corank in terms of elementary join maps.

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arXiv ID2105.04759 (version 2)
Pith IDBTY4USNI, Pith's permanent record of this paper and its review
CitationMaria Aparecida Soares Ruas, Maria Elenice Rodrigues Hernandes. "Join operation and ${\mathcal A}$-finite map-germs." arXiv:2105.04759 (2021). https://pith.science/paper/BTY4USNI
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,008 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.19 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this work we define some map-germs, called elementary joins, for the purpose of producing new ${\mathcal A}$-finite map-germs from them. In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{p},0)$ for $p\geq 2n$ of any corank in terms of elementary join maps. Our main tools are the delta invariant and some invariants of curves.

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 In this work we define some map-germs, called elementary joins, for the purpose of producing new ${\mathcal A}$-finite map-germs from them. contribution 1.00 0.95 0.14 asserted 1.00
s1 In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{p},0)$ for $p\geq 2n$ of any corank in terms of elementary join maps. contribution 0.54 0.94 0.44 asserted 1.00
s2 Our main tools are the delta invariant and some invariants of curves. method 1.00 0.56 0.04 asserted 0.99

What kind of paper the classifier reports this is: method or tool 0.59 · 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

In this work we define some map-germs, called elementary joins, for the purpose of producing new ${\mathcal A}$-finite map-germs from them. In particular, we describe a general form of an ${\mathcal A}$-finite monomial map from $(\mathbb{C}^n,0)$ to $(\mathbb{C}^{p},0)$ for $p\geq 2n$ of any corank in terms of elementary join maps. Our main tools are the delta invariant and some invariants of curves.

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