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Multiplicities of jumping points for mixed multiplier ideals

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Maria Alberich-Carramiñana, Josep Àlvarez Montaner, Ferran Dachs-Cadefau, Víctor González-Alonso

Algebraic Geometry · Submitted 25 Jul 2018

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

The authors' main claim We also introduce a Poincar\'e series for mixed multiplier ideals and prove its rationality.

how it is stated · asserted 1.00 read the record →

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arXiv ID1807.09839 (version 1)
Pith ID5HPRGOB7, Pith's permanent record of this paper and its review
CitationFerran Dachs-Cadefau, Josep \`Alvarez Montaner, Maria Alberich-Carrami\~nana, V\'ictor Gonz\'alez-Alonso. "Multiplicities of jumping points for mixed multiplier ideals." arXiv:1807.09839 (2018). https://pith.science/paper/5HPRGOB7
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,527 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. We also introduce a Poincar\'e series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.

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 paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. contribution 1.00 0.93 0.12 asserted 0.95
s1 In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. contribution 1.00 0.92 0.07 asserted 0.91
s2 We also introduce a Poincar\'e series for mixed multiplier ideals and prove its rationality. contribution 0.83 0.96 0.19 asserted 1.00
s3 Finally, we study the set of divisors that contribute to the log-canonical wall. contribution 0.99 0.93 0.09 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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  • references and citing sentences
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  • S sections
  • T body sentences
  • C citations
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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 paper we make a systematic study of the multiplicity of the jumping points associated to the mixed multiplier ideals of a family of ideals in a complex surface with rational singularities. In particular we study the behaviour of the multiplicity by small perturbations of the jumping points. We also introduce a Poincar\'e series for mixed multiplier ideals and prove its rationality. Finally, we study the set of divisors that contribute to the log-canonical wall.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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