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Counting stringy points on a family of character varieties

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Lucas de Amorin, Martin Mereb

Algebraic Geometry · Submitted 8 Nov 2024

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

The authors' main claim We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy.

how it is stated · asserted 1.00 read the record →

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arXiv ID2411.05563 (version 2)
Pith IDPMBH2YGQ, Pith's permanent record of this paper and its review
CitationLucas de Amorin, Martin Mereb. "Counting stringy points on a family of character varieties." arXiv:2411.05563 (2024). https://pith.science/paper/PMBH2YGQ
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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, 4,174 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.55 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups.

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 We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. result 0.77 0.93 0.77 asserted 1.00
s1 This leads to formulas for their stringy E-polynomials. result 0.94 0.87 0.19 asserted 1.00
s2 In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. interpretation 0.51 0.64 0.27 asserted 0.99
s3 Thaddeus, as well as a refinement regarding isotypic components. result 0.88 0.58 0.13 asserted 0.72
s4 Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups. method 1.00 0.89 0.05 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

We provide explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus and a refinement regarding isotypic components. Our proof is based on a Frobenius-type formula for Clifford-type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups.

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