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$\PGL$ orbits on products of flag varieties

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Izzet Coskun, Abuzer Gündüz

Algebraic Geometry · Submitted 6 Dec 2024

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

The authors' main claim We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$.

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arXiv ID2412.04870 (version 1)
Pith IDGCDFP6Y3, Pith's permanent record of this paper and its review
CitationAbuzer G\"und\"uz, Izzet Coskun. "$\PGL$ orbits on products of flag varieties." arXiv:2412.04870 (2024). https://pith.science/paper/GCDFP6Y3
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The compiled record

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, 2,981 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.06 · 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 study the existence of a dense orbit for the diagonal $\PGL(n)$ action on self-products of partial flag varieties. We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$. We also show that certain infinite families of products do not have a dense orbit.

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 study the existence of a dense orbit for the diagonal $\PGL(n)$ action on self-products of partial flag varieties. contribution 0.88 0.85 0.09 asserted 0.59
s1 We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$. result 0.84 0.95 0.58 asserted 1.00
s2 We also show that certain infinite families of products do not have a dense orbit. result 0.99 0.95 0.15 asserted 1.00

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

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 study the existence of a dense orbit for the diagonal $\PGL(n)$ action on self-products of partial flag varieties. We determine when there exists a dense orbit for flag varieties of the form $F(k_1, \dots, k_r; n)^m$ when $k_i = i$ or when $m=3$ and $k_i = \ell + i$ for some $\ell \geq 0$. We also show that certain infinite families of products do not have a dense orbit.

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